{"id":17045,"date":"2020-04-13T19:26:15","date_gmt":"2020-04-13T19:26:15","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/?post_type=chapter&p=17045"},"modified":"2020-05-21T05:31:19","modified_gmt":"2020-05-21T05:31:19","slug":"chapter-9-solutions-to-odd-numbered-problems","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/chapter\/chapter-9-solutions-to-odd-numbered-problems\/","title":{"raw":"Chapter 8 Solutions to Odd-Numbered Problems","rendered":"Chapter 8 Solutions to Odd-Numbered Problems"},"content":{"raw":"

Section 8.1 Solutions<\/h2>\r\n1.\u00a0No, you can either have zero, one, or infinitely many. Examine graphs.\r\n\r\n3.\u00a0This means there is no realistic break-even point. By the time the company produces one unit they are already making profit.\r\n\r\n5.\u00a0You can solve by substitution (isolating [latex]x[\/latex] or [latex]y[\/latex] ), graphically, or by addition.\r\n\r\n7.\u00a0Yes\r\n\r\n9.\u00a0Yes\r\n\r\n11.\u00a0[latex]\\left(-1,2\\right)[\/latex]\r\n\r\n13.\u00a0[latex]\\left(-3,1\\right)[\/latex]\r\n\r\n15.\u00a0[latex]\\left(-\\frac{3}{5},0\\right)[\/latex]\r\n\r\n17.\u00a0No solutions exist.\r\n\r\n19.\u00a0[latex]\\left(\\frac{72}{5},\\frac{132}{5}\\right)[\/latex]\r\n\r\n21.\u00a0[latex]\\left(6,-6\\right)[\/latex]\r\n\r\n23.\u00a0[latex]\\left(-\\frac{1}{2},\\frac{1}{10}\\right)[\/latex]\r\n\r\n25.\u00a0No solutions exist.\r\n\r\n27.\u00a0[latex]\\left(-\\frac{1}{5},\\frac{2}{3}\\right)[\/latex]\r\n\r\n29.\u00a0[latex]\\left(x,\\frac{x+3}{2}\\right)[\/latex]\r\n\r\n31.\u00a0[latex]\\left(-4,4\\right)[\/latex]\r\n\r\n33.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{8}\\right)[\/latex]\r\n\r\n35.\u00a0[latex]\\left(\\frac{1}{6},0\\right)[\/latex]\r\n\r\n37.\u00a0[latex]\\left(x,2\\left(7x - 6\\right)\\right)[\/latex]\r\n\r\n39.\u00a0[latex]\\left(-\\frac{5}{6},\\frac{4}{3}\\right)[\/latex]\r\n\r\n41.\u00a0Consistent with one solution\r\n\r\n43.\u00a0Consistent with one solution\r\n\r\n45.\u00a0Dependent with infinitely many solutions\r\n\r\n47.\u00a0[latex]\\left(-3.08,4.91\\right)[\/latex]\r\n\r\n49.\u00a0[latex]\\left(-1.52,2.29\\right)[\/latex]\r\n\r\n51.\u00a0[latex]\\left(\\frac{A+B}{2},\\frac{A-B}{2}\\right)[\/latex]\r\n\r\n53.\u00a0[latex]\\left(\\frac{-1}{A-B},\\frac{A}{A-B}\\right)[\/latex]\r\n\r\n55.\u00a0[latex]\\left(\\frac{CE-BF}{BD-AE},\\frac{AF-CD}{BD-AE}\\right)[\/latex]\r\n\r\n57.\u00a0They never turn a profit.\r\n\r\n59.\u00a0[latex]\\left(1,250,100,000\\right)[\/latex]\r\n\r\n61.\u00a0The numbers are 7.5 and 20.5.\r\n\r\n63.\u00a024,000\r\n\r\n65.\u00a0790 sophomores, 805 freshman\r\n\r\n67.\u00a056 men, 74 women\r\n\r\n69.\u00a010 gallons of 10% solution, 15 gallons of 60% solution\r\n\r\n71.\u00a0Swan Peak: $750,000, Riverside: $350,000\r\n\r\n73.\u00a0$12,500 in the first account, $10,500 in the second account.\r\n\r\n75.\u00a0High-tops: 45, Low-tops: 15\r\n\r\n77.\u00a0Infinitely many solutions. We need more information.\r\n

Section 8.2 Solutions<\/h2>\r\n1.\u00a0A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions.\r\n\r\n3.\u00a0No. There does not need to be a feasible region. Consider a system that is bounded by two parallel lines. One inequality represents the region above the upper line; the other represents the region below the lower line. In this case, no points in the plane are located in both regions; hence there is no feasible region.\r\n\r\n5.\u00a0Choose any number between each solution and plug into [latex]C\\left(x\\right)[\/latex] and [latex]R\\left(x\\right)[\/latex]. If [latex]C\\left(x\\right)<R\\left(x\\right),\\text{}[\/latex] then there is profit.\r\n\r\n7.\u00a0[latex]\\left(0,-3\\right),\\left(3,0\\right)[\/latex]\r\n\r\n9.\u00a0[latex]\\left(-\\frac{3\\sqrt{2}}{2},\\frac{3\\sqrt{2}}{2}\\right),\\left(\\frac{3\\sqrt{2}}{2},-\\frac{3\\sqrt{2}}{2}\\right)[\/latex]\r\n\r\n11.\u00a0[latex]\\left(-3,0\\right),\\left(3,0\\right)[\/latex]\r\n\r\n13.\u00a0[latex]\\left(\\frac{1}{4},-\\frac{\\sqrt{62}}{8}\\right),\\left(\\frac{1}{4},\\frac{\\sqrt{62}}{8}\\right)[\/latex]\r\n\r\n15.\u00a0[latex]\\left(-\\frac{\\sqrt{398}}{4},\\frac{199}{4}\\right),\\left(\\frac{\\sqrt{398}}{4},\\frac{199}{4}\\right)[\/latex]\r\n\r\n17.\u00a0[latex]\\left(0,2\\right),\\left(1,3\\right)[\/latex]\r\n\r\n19.\u00a0[latex]\\left(-\\sqrt{\\frac{1}{2}\\left(\\sqrt{5}-1\\right)},\\frac{1}{2}\\left(1-\\sqrt{5}\\right)\\right),\\left(\\sqrt{\\frac{1}{2}\\left(\\sqrt{5}-1\\right)},\\frac{1}{2}\\left(1-\\sqrt{5}\\right)\\right)[\/latex]\r\n\r\n21.\u00a0[latex]\\left(5,0\\right)[\/latex]\r\n\r\n23.\u00a0[latex]\\left(0,0\\right)[\/latex]\r\n\r\n25.\u00a0[latex]\\left(3,0\\right)[\/latex]\r\n\r\n27.\u00a0No Solutions Exist\r\n\r\n29.\u00a0No Solutions Exist\r\n\r\n31.\u00a0[latex]\\left(-\\frac{\\sqrt{2}}{2},-\\frac{\\sqrt{2}}{2}\\right),\\left(-\\frac{\\sqrt{2}}{2},\\frac{\\sqrt{2}}{2}\\right),\\left(\\frac{\\sqrt{2}}{2},-\\frac{\\sqrt{2}}{2}\\right),\\left(\\frac{\\sqrt{2}}{2},\\frac{\\sqrt{2}}{2}\\right)[\/latex]\r\n\r\n33.\u00a0[latex]\\left(2,0\\right)[\/latex]\r\n\r\n35.\u00a0[latex]\\left(-\\sqrt{7},-3\\right),\\left(-\\sqrt{7},3\\right),\\left(\\sqrt{7},-3\\right),\\left(\\sqrt{7},3\\right)[\/latex]\r\n\r\n37.\u00a0[latex]\\left(-\\sqrt{\\frac{1}{2}\\left(\\sqrt{73}-5\\right)},\\frac{1}{2}\\left(7-\\sqrt{73}\\right)\\right),\\left(\\sqrt{\\frac{1}{2}\\left(\\sqrt{73}-5\\right)},\\frac{1}{2}\\left(7-\\sqrt{73}\\right)\\right)[\/latex]\r\n\r\n39.\r\n\"A\r\n\r\n41.\r\n\"A\r\n\r\n43.\r\n\"Two\r\n\r\n45.\r\n\"Two\r\n\r\n47.\r\n\"Two\r\n\r\n49.\u00a0[latex]\\left(-2\\sqrt{\\frac{70}{383}},-2\\sqrt{\\frac{35}{29}}\\right),\\left(-2\\sqrt{\\frac{70}{383}},2\\sqrt{\\frac{35}{29}}\\right),\\left(2\\sqrt{\\frac{70}{383}},-2\\sqrt{\\frac{35}{29}}\\right),\\left(2\\sqrt{\\frac{70}{383}},2\\sqrt{\\frac{35}{29}}\\right)[\/latex]\r\n\r\n51.\u00a0No Solution Exists\r\n\r\n53.\u00a0[latex]x=0,y>0[\/latex] and [latex]0<x<1,\\sqrt{x}<y<\\frac{1}{x}[\/latex]\r\n\r\n55.\u00a012, 288\r\n\r\n57.\u00a02\u201320 computers\r\n

Section 8.3 Solutions<\/h2>\r\n1.\u00a0No, a quotient of polynomials can only be decomposed if the denominator can be factored. For example, [latex]\\frac{1}{{x}^{2}+1}[\/latex] cannot be decomposed because the denominator cannot be factored.\r\n\r\n3.\u00a0Graph both sides and ensure they are equal.\r\n\r\n5.\u00a0If we choose [latex]x=-1[\/latex], then the B<\/em>-term disappears, letting us immediately know that [latex]A=3[\/latex]. We could alternatively plug in [latex]x=-\\frac{5}{3}[\/latex], giving us a B<\/em>-value of [latex]-2[\/latex].\r\n\r\n7.\u00a0[latex]\\frac{8}{x+3}-\\frac{5}{x - 8}[\/latex]\r\n\r\n9.\u00a0[latex]\\frac{1}{x+5}+\\frac{9}{x+2}[\/latex]\r\n\r\n11.\u00a0[latex]\\frac{3}{5x - 2}+\\frac{4}{4x - 1}[\/latex]\r\n\r\n13.\u00a0[latex]\\frac{5}{2\\left(x+3\\right)}+\\frac{5}{2\\left(x - 3\\right)}[\/latex]\r\n\r\n15.\u00a0[latex]\\frac{3}{x+2}+\\frac{3}{x - 2}[\/latex]\r\n\r\n17.\u00a0[latex]\\frac{9}{5\\left(x+2\\right)}+\\frac{11}{5\\left(x - 3\\right)}[\/latex]\r\n\r\n19.\u00a0[latex]\\frac{8}{x - 3}-\\frac{5}{x - 2}[\/latex]\r\n\r\n21.\u00a0[latex]\\frac{1}{x - 2}+\\frac{2}{{\\left(x - 2\\right)}^{2}}[\/latex]\r\n\r\n23.\u00a0[latex]-\\frac{6}{4x+5}+\\frac{3}{{\\left(4x+5\\right)}^{2}}[\/latex]\r\n\r\n25.\u00a0[latex]-\\frac{1}{x - 7}-\\frac{2}{{\\left(x - 7\\right)}^{2}}[\/latex]\r\n\r\n27.\u00a0[latex]\\frac{4}{x}-\\frac{3}{2\\left(x+1\\right)}+\\frac{7}{2{\\left(x+1\\right)}^{2}}[\/latex]\r\n\r\n29.\u00a0[latex]\\frac{4}{x}+\\frac{2}{{x}^{2}}-\\frac{3}{3x+2}+\\frac{7}{2{\\left(3x+2\\right)}^{2}}[\/latex]\r\n\r\n31.\u00a0[latex]\\frac{x+1}{{x}^{2}+x+3}+\\frac{3}{x+2}[\/latex]\r\n\r\n33.\u00a0[latex]\\frac{4 - 3x}{{x}^{2}+3x+8}+\\frac{1}{x - 1}[\/latex]\r\n\r\n35.\u00a0[latex]\\frac{2x - 1}{{x}^{2}+6x+1}+\\frac{2}{x+3}[\/latex]\r\n\r\n37.\u00a0[latex]\\frac{1}{{x}^{2}+x+1}+\\frac{4}{x - 1}[\/latex]\r\n\r\n39.\u00a0[latex]\\frac{2}{{x}^{2}-3x+9}+\\frac{3}{x+3}[\/latex]\r\n\r\n41.\u00a0[latex]-\\frac{1}{4{x}^{2}+6x+9}+\\frac{1}{2x - 3}[\/latex]\r\n\r\n43.\u00a0[latex]\\frac{1}{x}+\\frac{1}{x+6}-\\frac{4x}{{x}^{2}-6x+36}[\/latex]\r\n\r\n45.\u00a0[latex]\\frac{x+6}{{x}^{2}+1}+\\frac{4x+3}{{\\left({x}^{2}+1\\right)}^{2}}[\/latex]\r\n\r\n47.\u00a0[latex]\\frac{x+1}{x+2}+\\frac{2x+3}{{\\left(x+2\\right)}^{2}}[\/latex]\r\n\r\n49.\u00a0[latex]\\frac{1}{{x}^{2}+3x+25}-\\frac{3x}{{\\left({x}^{2}+3x+25\\right)}^{2}}[\/latex]\r\n\r\n51.\u00a0[latex]\\frac{1}{8x}-\\frac{x}{8\\left({x}^{2}+4\\right)}+\\frac{10-x}{2{\\left({x}^{2}+4\\right)}^{2}}[\/latex]\r\n\r\n53.\u00a0[latex]-\\frac{16}{x}-\\frac{9}{{x}^{2}}+\\frac{16}{x - 1}-\\frac{7}{{\\left(x - 1\\right)}^{2}}[\/latex]\r\n\r\n55.\u00a0[latex]\\frac{1}{x+1}-\\frac{2}{{\\left(x+1\\right)}^{2}}+\\frac{5}{{\\left(x+1\\right)}^{3}}[\/latex]\r\n\r\n57.\u00a0[latex]\\frac{5}{x - 2}-\\frac{3}{10\\left(x+2\\right)}+\\frac{7}{x+8}-\\frac{7}{10\\left(x - 8\\right)}[\/latex]\r\n\r\n59.\u00a0[latex]-\\frac{5}{4x}-\\frac{5}{2\\left(x+2\\right)}+\\frac{11}{2\\left(x+4\\right)}+\\frac{5}{4\\left(x+4\\right)}[\/latex]","rendered":"

Section 8.1 Solutions<\/h2>\n

1.\u00a0No, you can either have zero, one, or infinitely many. Examine graphs.<\/p>\n

3.\u00a0This means there is no realistic break-even point. By the time the company produces one unit they are already making profit.<\/p>\n

5.\u00a0You can solve by substitution (isolating [latex]x[\/latex] or [latex]y[\/latex] ), graphically, or by addition.<\/p>\n

7.\u00a0Yes<\/p>\n

9.\u00a0Yes<\/p>\n

11.\u00a0[latex]\\left(-1,2\\right)[\/latex]<\/p>\n

13.\u00a0[latex]\\left(-3,1\\right)[\/latex]<\/p>\n

15.\u00a0[latex]\\left(-\\frac{3}{5},0\\right)[\/latex]<\/p>\n

17.\u00a0No solutions exist.<\/p>\n

19.\u00a0[latex]\\left(\\frac{72}{5},\\frac{132}{5}\\right)[\/latex]<\/p>\n

21.\u00a0[latex]\\left(6,-6\\right)[\/latex]<\/p>\n

23.\u00a0[latex]\\left(-\\frac{1}{2},\\frac{1}{10}\\right)[\/latex]<\/p>\n

25.\u00a0No solutions exist.<\/p>\n

27.\u00a0[latex]\\left(-\\frac{1}{5},\\frac{2}{3}\\right)[\/latex]<\/p>\n

29.\u00a0[latex]\\left(x,\\frac{x+3}{2}\\right)[\/latex]<\/p>\n

31.\u00a0[latex]\\left(-4,4\\right)[\/latex]<\/p>\n

33.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{8}\\right)[\/latex]<\/p>\n

35.\u00a0[latex]\\left(\\frac{1}{6},0\\right)[\/latex]<\/p>\n

37.\u00a0[latex]\\left(x,2\\left(7x - 6\\right)\\right)[\/latex]<\/p>\n

39.\u00a0[latex]\\left(-\\frac{5}{6},\\frac{4}{3}\\right)[\/latex]<\/p>\n

41.\u00a0Consistent with one solution<\/p>\n

43.\u00a0Consistent with one solution<\/p>\n

45.\u00a0Dependent with infinitely many solutions<\/p>\n

47.\u00a0[latex]\\left(-3.08,4.91\\right)[\/latex]<\/p>\n

49.\u00a0[latex]\\left(-1.52,2.29\\right)[\/latex]<\/p>\n

51.\u00a0[latex]\\left(\\frac{A+B}{2},\\frac{A-B}{2}\\right)[\/latex]<\/p>\n

53.\u00a0[latex]\\left(\\frac{-1}{A-B},\\frac{A}{A-B}\\right)[\/latex]<\/p>\n

55.\u00a0[latex]\\left(\\frac{CE-BF}{BD-AE},\\frac{AF-CD}{BD-AE}\\right)[\/latex]<\/p>\n

57.\u00a0They never turn a profit.<\/p>\n

59.\u00a0[latex]\\left(1,250,100,000\\right)[\/latex]<\/p>\n

61.\u00a0The numbers are 7.5 and 20.5.<\/p>\n

63.\u00a024,000<\/p>\n

65.\u00a0790 sophomores, 805 freshman<\/p>\n

67.\u00a056 men, 74 women<\/p>\n

69.\u00a010 gallons of 10% solution, 15 gallons of 60% solution<\/p>\n

71.\u00a0Swan Peak: $750,000, Riverside: $350,000<\/p>\n

73.\u00a0$12,500 in the first account, $10,500 in the second account.<\/p>\n

75.\u00a0High-tops: 45, Low-tops: 15<\/p>\n

77.\u00a0Infinitely many solutions. We need more information.<\/p>\n

Section 8.2 Solutions<\/h2>\n

1.\u00a0A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions.<\/p>\n

3.\u00a0No. There does not need to be a feasible region. Consider a system that is bounded by two parallel lines. One inequality represents the region above the upper line; the other represents the region below the lower line. In this case, no points in the plane are located in both regions; hence there is no feasible region.<\/p>\n

5.\u00a0Choose any number between each solution and plug into [latex]C\\left(x\\right)[\/latex] and [latex]R\\left(x\\right)[\/latex]. If [latex]C\\left(x\\right)<\/p>\n

41.
\n\"A<\/p>\n

43.
\n\"Two<\/p>\n

45.
\n\"Two<\/p>\n

47.
\n\"Two<\/p>\n

49.\u00a0[latex]\\left(-2\\sqrt{\\frac{70}{383}},-2\\sqrt{\\frac{35}{29}}\\right),\\left(-2\\sqrt{\\frac{70}{383}},2\\sqrt{\\frac{35}{29}}\\right),\\left(2\\sqrt{\\frac{70}{383}},-2\\sqrt{\\frac{35}{29}}\\right),\\left(2\\sqrt{\\frac{70}{383}},2\\sqrt{\\frac{35}{29}}\\right)[\/latex]<\/p>\n

51.\u00a0No Solution Exists<\/p>\n

53.\u00a0[latex]x=0,y>0[\/latex] and [latex]0Section 8.3 Solutions<\/h2>\n

1.\u00a0No, a quotient of polynomials can only be decomposed if the denominator can be factored. For example, [latex]\\frac{1}{{x}^{2}+1}[\/latex] cannot be decomposed because the denominator cannot be factored.<\/p>\n

3.\u00a0Graph both sides and ensure they are equal.<\/p>\n

5.\u00a0If we choose [latex]x=-1[\/latex], then the B<\/em>-term disappears, letting us immediately know that [latex]A=3[\/latex]. We could alternatively plug in [latex]x=-\\frac{5}{3}[\/latex], giving us a B<\/em>-value of [latex]-2[\/latex].<\/p>\n

7.\u00a0[latex]\\frac{8}{x+3}-\\frac{5}{x - 8}[\/latex]<\/p>\n

9.\u00a0[latex]\\frac{1}{x+5}+\\frac{9}{x+2}[\/latex]<\/p>\n

11.\u00a0[latex]\\frac{3}{5x - 2}+\\frac{4}{4x - 1}[\/latex]<\/p>\n

13.\u00a0[latex]\\frac{5}{2\\left(x+3\\right)}+\\frac{5}{2\\left(x - 3\\right)}[\/latex]<\/p>\n

15.\u00a0[latex]\\frac{3}{x+2}+\\frac{3}{x - 2}[\/latex]<\/p>\n

17.\u00a0[latex]\\frac{9}{5\\left(x+2\\right)}+\\frac{11}{5\\left(x - 3\\right)}[\/latex]<\/p>\n

19.\u00a0[latex]\\frac{8}{x - 3}-\\frac{5}{x - 2}[\/latex]<\/p>\n

21.\u00a0[latex]\\frac{1}{x - 2}+\\frac{2}{{\\left(x - 2\\right)}^{2}}[\/latex]<\/p>\n

23.\u00a0[latex]-\\frac{6}{4x+5}+\\frac{3}{{\\left(4x+5\\right)}^{2}}[\/latex]<\/p>\n

25.\u00a0[latex]-\\frac{1}{x - 7}-\\frac{2}{{\\left(x - 7\\right)}^{2}}[\/latex]<\/p>\n

27.\u00a0[latex]\\frac{4}{x}-\\frac{3}{2\\left(x+1\\right)}+\\frac{7}{2{\\left(x+1\\right)}^{2}}[\/latex]<\/p>\n

29.\u00a0[latex]\\frac{4}{x}+\\frac{2}{{x}^{2}}-\\frac{3}{3x+2}+\\frac{7}{2{\\left(3x+2\\right)}^{2}}[\/latex]<\/p>\n

31.\u00a0[latex]\\frac{x+1}{{x}^{2}+x+3}+\\frac{3}{x+2}[\/latex]<\/p>\n

33.\u00a0[latex]\\frac{4 - 3x}{{x}^{2}+3x+8}+\\frac{1}{x - 1}[\/latex]<\/p>\n

35.\u00a0[latex]\\frac{2x - 1}{{x}^{2}+6x+1}+\\frac{2}{x+3}[\/latex]<\/p>\n

37.\u00a0[latex]\\frac{1}{{x}^{2}+x+1}+\\frac{4}{x - 1}[\/latex]<\/p>\n

39.\u00a0[latex]\\frac{2}{{x}^{2}-3x+9}+\\frac{3}{x+3}[\/latex]<\/p>\n

41.\u00a0[latex]-\\frac{1}{4{x}^{2}+6x+9}+\\frac{1}{2x - 3}[\/latex]<\/p>\n

43.\u00a0[latex]\\frac{1}{x}+\\frac{1}{x+6}-\\frac{4x}{{x}^{2}-6x+36}[\/latex]<\/p>\n

45.\u00a0[latex]\\frac{x+6}{{x}^{2}+1}+\\frac{4x+3}{{\\left({x}^{2}+1\\right)}^{2}}[\/latex]<\/p>\n

47.\u00a0[latex]\\frac{x+1}{x+2}+\\frac{2x+3}{{\\left(x+2\\right)}^{2}}[\/latex]<\/p>\n

49.\u00a0[latex]\\frac{1}{{x}^{2}+3x+25}-\\frac{3x}{{\\left({x}^{2}+3x+25\\right)}^{2}}[\/latex]<\/p>\n

51.\u00a0[latex]\\frac{1}{8x}-\\frac{x}{8\\left({x}^{2}+4\\right)}+\\frac{10-x}{2{\\left({x}^{2}+4\\right)}^{2}}[\/latex]<\/p>\n

53.\u00a0[latex]-\\frac{16}{x}-\\frac{9}{{x}^{2}}+\\frac{16}{x - 1}-\\frac{7}{{\\left(x - 1\\right)}^{2}}[\/latex]<\/p>\n

55.\u00a0[latex]\\frac{1}{x+1}-\\frac{2}{{\\left(x+1\\right)}^{2}}+\\frac{5}{{\\left(x+1\\right)}^{3}}[\/latex]<\/p>\n

57.\u00a0[latex]\\frac{5}{x - 2}-\\frac{3}{10\\left(x+2\\right)}+\\frac{7}{x+8}-\\frac{7}{10\\left(x - 8\\right)}[\/latex]<\/p>\n

59.\u00a0[latex]-\\frac{5}{4x}-\\frac{5}{2\\left(x+2\\right)}+\\frac{11}{2\\left(x+4\\right)}+\\frac{5}{4\\left(x+4\\right)}[\/latex]<\/p>\n","protected":false},"author":264444,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-17045","chapter","type-chapter","status-publish","hentry"],"part":16602,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/pressbooks\/v2\/chapters\/17045","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/wp\/v2\/users\/264444"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/pressbooks\/v2\/chapters\/17045\/revisions"}],"predecessor-version":[{"id":17644,"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/pressbooks\/v2\/chapters\/17045\/revisions\/17644"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/pressbooks\/v2\/parts\/16602"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/pressbooks\/v2\/chapters\/17045\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/wp\/v2\/media?parent=17045"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=17045"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/wp\/v2\/contributor?post=17045"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-precalculus\/wp-json\/wp\/v2\/license?post=17045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}