{"id":1944,"date":"2021-12-02T19:40:07","date_gmt":"2021-12-03T00:40:07","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-4\/"},"modified":"2022-11-02T10:38:36","modified_gmt":"2022-11-02T14:38:36","slug":"answer-key-8-4","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-4\/","title":{"raw":"Answer Key 8.4","rendered":"Answer Key 8.4"},"content":{"raw":"
    \n \t
  1. [latex]\\dfrac{2+4}{a+3}=\\dfrac{6}{a+3}[\/latex]<\/li>\n \t
  2. [latex]\\dfrac{x^2-(6x-8)}{x-2}\\Rightarrow \\dfrac{x^2-6x+8}{x-2}\\Rightarrow \\dfrac{(x-4)\\cancel{(x-2)}}{\\cancel{(x-2)}}\\Rightarrow x-4[\/latex]<\/li>\n \t
  3. [latex]\\dfrac{t^2+4t+2t-7}{t-1}\\Rightarrow \\dfrac{t^2+6t-7}{t-1}\\Rightarrow \\dfrac{(t+7)\\cancel{(t-1)}}{\\cancel{(t-1)}}\\Rightarrow t+7[\/latex]<\/li>\n \t
  4. [latex]\\dfrac{a^2+3a-4}{a^2+5a-6}\\Rightarrow \\dfrac{(a+4)\\cancel{(a-1)}}{(a+6)\\cancel{(a-1)}}\\Rightarrow \\dfrac{a+4}{a+6}[\/latex]<\/li>\n \t
  5. [latex]\\text{LCD}=24r\\hspace{0.25in} \\dfrac{5}{6r}\\cdot \\dfrac{4}{4}-\\dfrac{5}{8r}\\cdot \\dfrac{3}{3}\\Rightarrow \\dfrac{20}{24r}-\\dfrac{15}{24r}\\Rightarrow \\dfrac{5}{24r}[\/latex]<\/li>\n \t
  6. [latex]\\text{LCD}=x^2y^2\\hspace{0.25in} \\dfrac{7}{xy^2}\\cdot \\dfrac{x}{x}+\\dfrac{3}{x^2y}\\cdot \\dfrac{y}{y}\\Rightarrow \\dfrac{7x+3y}{x^2y^2}[\/latex]<\/li>\n \t
  7. [latex]\\text{LCD}=18t^3\\hspace{0.25in} \\dfrac{8}{9t^3}\\cdot \\dfrac{2}{2}+\\dfrac{5}{6t^2}\\cdot \\dfrac{3t}{3t}\\Rightarrow \\dfrac{15t+16}{18t^3}[\/latex]<\/li>\n \t
  8. [latex]\\text{LCD}=24\\hspace{0.25in} \\dfrac{(x+5)(3)}{(8)(3)}+\\dfrac{(x-3)(2)}{(12)(2)}\\Rightarrow \\dfrac{3x+15+2x-6}{24}\\Rightarrow \\dfrac{5x+9}{24}[\/latex]<\/li>\n \t
  9. [latex]\\text{LCD}=4x \\hspace{0.25in} \\dfrac{x-1}{4x}-\\dfrac{4(2x+3)}{4\\cdot x}\\Rightarrow \\dfrac{x-1-8x-12}{4x}\\Rightarrow \\dfrac{-7x-13}{4x}[\/latex]<\/li>\n \t
  10. [latex]\\text{LCD}=c^2d^2 \\hspace{0.25in} \\dfrac{(2c-d)(d)}{c^2d(d)}-\\dfrac{(c+d)(c)}{cd^2(c)}\\Rightarrow \\dfrac{2cd-d^2-c^2-cd}{c^2d^2}\\Rightarrow \\dfrac{cd-c^2-d^2}{c^2d^2}[\/latex]<\/li>\n \t
  11. [latex]\\text{LCD}=2x^2y^2 \\hspace{0.25in} \\dfrac{(5x+3y)(y)}{(2x^2y)(y)}-\\dfrac{(3x+4y)(2x)}{(xy^2)(2x)}\\Rightarrow \\dfrac{5xy+3y^2-6x^2-8xy}{2x^2y^2}\\Rightarrow[\/latex]\n[latex]\\dfrac{3y^2-3xy-6x^2}{2x^2y^2}[\/latex]<\/li>\n \t
  12. [latex]\\text{LCD} = (x - 1)(x + 1)\\hspace{0.25in} \\dfrac{2(x+1)}{(x-1)(x+1)}+\\dfrac{2(x-1)}{(x+1)(x-1)}\\Rightarrow \\dfrac{2x+2+2x-2}{(x+1)(x-1)}\\Rightarrow[\/latex]\n[latex]\\dfrac{4x}{(x+1)(x-1)}[\/latex]<\/li>\n \t
  13. [latex]\\text{LCD}=(x+3)(x+2)(x+1)\\hspace{0.25in} \\dfrac{x(x+1)}{(x+3)(x+2)(x+1)}-\\dfrac{2(x+3)}{(x+3)(x+2)(x+1)}[\/latex]\n[latex]\\Rightarrow\\dfrac{x^2+x-2x-6}{(x+3)(x+2)(x+1)}\\Rightarrow \\dfrac{x^2-x-6}{(x+3)(x+2)(x+1)}\\Rightarrow \\dfrac{(x-3)\\cancel{(x+2)}}{(x+3)\\cancel{(x+2)}(x+1)}[\/latex]\n[latex]\\Rightarrow\\dfrac{x-3}{(x+3)(x+1)}[\/latex]<\/li>\n \t
  14. [latex]\\text{LCD}=(x-1)(x+1)(x+4) \\hspace{0.25in} \\dfrac{2x(x+4)}{(x-1)(x+1)(x+4)}-\\dfrac{3(x-1)}{(x-1)(x+1)(x+4)}[\/latex]\n[latex]\\Rightarrow\\dfrac{2x^2+8x-3x+3}{(x-1)(x+1)(x+4)}\\Rightarrow \\dfrac{2x^2+5x+3}{(x-1)(x+1)(x+4)}\\Rightarrow \\dfrac{(2x+3)\\cancel{(x+1)}}{(x-1)\\cancel{(x+1)}(x+4)}[\/latex]\n[latex]\\Rightarrow\\dfrac{2x+3}{(x-1)(x+4)}[\/latex]<\/li>\n \t
  15. [latex]\\text{LCD}=(x+7)(x+8)(x+6) \\hspace{0.25in} \\dfrac{x(x+6)}{(x+7)(x+8)(x+6)}-\\dfrac{7(x+8)}{(x+7)(x+8)(x+6)}[\/latex]\n[latex]\\Rightarrow \\dfrac{x^2+6x-7x-56}{(x+7)(x+8)(x+6)}\\Rightarrow\\dfrac{x^2-x-56}{(x+7)(x+8)(x+6)}\\Rightarrow\\dfrac{(x-8)\\cancel{(x+7)}}{\\cancel{(x+7)}(x+8)(x+6)}[\/latex]\n[latex]\\Rightarrow\\dfrac{x-8}{(x+8)(x+6)}[\/latex]<\/li>\n \t
  16. [latex]\\text{LCD}=(x-3)(x+3)(x-2) \\hspace{0.25in} \\dfrac{2x(x-2)}{(x-3)(x+3)(x-2)}+\\dfrac{5(x-3)}{(x-3)(x+3)(x-2)}[\/latex]\n[latex]\\Rightarrow\\dfrac{2x^2-4x+5x-15}{(x-3)(x+3)(x-2)}\\Rightarrow \\dfrac{2x^2+x-15}{(x-3)(x+3)(x-2)}\\Rightarrow \\dfrac{\\cancel{(x+3)}(2x-5)}{(x-3)\\cancel{(x+3)}(x-2)}[\/latex]\n[latex]\\Rightarrow\\dfrac{2x-5}{(x-3)(x-2)}[\/latex]<\/li>\n \t
  17. [latex]\\text{LCD}=(x-3)(x+2)(x+3) \\hspace{0.25in} \\dfrac{5x(x+3)}{(x-3)(x+2)(x+3)}-\\dfrac{18(x+2)}{(x-3)(x+2)(x+3)}[\/latex]\n[latex]\\Rightarrow\\dfrac{5x^2+15x-18x-36}{(x-3)(x+2)(x+3)}\\Rightarrow \\dfrac{5x^2-3x-36}{(x-3)(x+2)(x+3)}\\Rightarrow \\dfrac{\\cancel{(x-3)}(5x+12)}{\\cancel{(x-3)}(x+2)(x+3)}[\/latex]\n[latex]\\Rightarrow\\dfrac{5x+12}{(x+2)(x+3)}[\/latex]<\/li>\n \t
  18. [latex]\\text{LCD}=(x-3)(x+1)(x-2) \\hspace{0.25in} \\dfrac{4x(x-2)}{(x-3)(x+1)(x-2)}-\\dfrac{3(x+1)}{(x-3)(x+1)(x-2)}[\/latex]\n[latex]\\Rightarrow\\dfrac{4x^2-8x-3x-3}{(x-3)(x+1)(x-2)}\\Rightarrow \\dfrac{4x^2-11x-3}{(x-3)(x+1)(x-2)}\\Rightarrow \\dfrac{(4x+1)\\cancel{(x-3)}}{\\cancel{(x-3)}(x+1)(x-2)}[\/latex]\n[latex]\\Rightarrow\\dfrac{4x+1}{(x+1)(x-2)}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\dfrac{2+4}{a+3}=\\dfrac{6}{a+3}[\/latex]<\/li>\n
    2. [latex]\\dfrac{x^2-(6x-8)}{x-2}\\Rightarrow \\dfrac{x^2-6x+8}{x-2}\\Rightarrow \\dfrac{(x-4)\\cancel{(x-2)}}{\\cancel{(x-2)}}\\Rightarrow x-4[\/latex]<\/li>\n
    3. [latex]\\dfrac{t^2+4t+2t-7}{t-1}\\Rightarrow \\dfrac{t^2+6t-7}{t-1}\\Rightarrow \\dfrac{(t+7)\\cancel{(t-1)}}{\\cancel{(t-1)}}\\Rightarrow t+7[\/latex]<\/li>\n
    4. [latex]\\dfrac{a^2+3a-4}{a^2+5a-6}\\Rightarrow \\dfrac{(a+4)\\cancel{(a-1)}}{(a+6)\\cancel{(a-1)}}\\Rightarrow \\dfrac{a+4}{a+6}[\/latex]<\/li>\n
    5. [latex]\\text{LCD}=24r\\hspace{0.25in} \\dfrac{5}{6r}\\cdot \\dfrac{4}{4}-\\dfrac{5}{8r}\\cdot \\dfrac{3}{3}\\Rightarrow \\dfrac{20}{24r}-\\dfrac{15}{24r}\\Rightarrow \\dfrac{5}{24r}[\/latex]<\/li>\n
    6. [latex]\\text{LCD}=x^2y^2\\hspace{0.25in} \\dfrac{7}{xy^2}\\cdot \\dfrac{x}{x}+\\dfrac{3}{x^2y}\\cdot \\dfrac{y}{y}\\Rightarrow \\dfrac{7x+3y}{x^2y^2}[\/latex]<\/li>\n
    7. [latex]\\text{LCD}=18t^3\\hspace{0.25in} \\dfrac{8}{9t^3}\\cdot \\dfrac{2}{2}+\\dfrac{5}{6t^2}\\cdot \\dfrac{3t}{3t}\\Rightarrow \\dfrac{15t+16}{18t^3}[\/latex]<\/li>\n
    8. [latex]\\text{LCD}=24\\hspace{0.25in} \\dfrac{(x+5)(3)}{(8)(3)}+\\dfrac{(x-3)(2)}{(12)(2)}\\Rightarrow \\dfrac{3x+15+2x-6}{24}\\Rightarrow \\dfrac{5x+9}{24}[\/latex]<\/li>\n
    9. [latex]\\text{LCD}=4x \\hspace{0.25in} \\dfrac{x-1}{4x}-\\dfrac{4(2x+3)}{4\\cdot x}\\Rightarrow \\dfrac{x-1-8x-12}{4x}\\Rightarrow \\dfrac{-7x-13}{4x}[\/latex]<\/li>\n
    10. [latex]\\text{LCD}=c^2d^2 \\hspace{0.25in} \\dfrac{(2c-d)(d)}{c^2d(d)}-\\dfrac{(c+d)(c)}{cd^2(c)}\\Rightarrow \\dfrac{2cd-d^2-c^2-cd}{c^2d^2}\\Rightarrow \\dfrac{cd-c^2-d^2}{c^2d^2}[\/latex]<\/li>\n
    11. [latex]\\text{LCD}=2x^2y^2 \\hspace{0.25in} \\dfrac{(5x+3y)(y)}{(2x^2y)(y)}-\\dfrac{(3x+4y)(2x)}{(xy^2)(2x)}\\Rightarrow \\dfrac{5xy+3y^2-6x^2-8xy}{2x^2y^2}\\Rightarrow[\/latex]
      \n[latex]\\dfrac{3y^2-3xy-6x^2}{2x^2y^2}[\/latex]<\/li>\n
    12. [latex]\\text{LCD} = (x - 1)(x + 1)\\hspace{0.25in} \\dfrac{2(x+1)}{(x-1)(x+1)}+\\dfrac{2(x-1)}{(x+1)(x-1)}\\Rightarrow \\dfrac{2x+2+2x-2}{(x+1)(x-1)}\\Rightarrow[\/latex]
      \n[latex]\\dfrac{4x}{(x+1)(x-1)}[\/latex]<\/li>\n
    13. [latex]\\text{LCD}=(x+3)(x+2)(x+1)\\hspace{0.25in} \\dfrac{x(x+1)}{(x+3)(x+2)(x+1)}-\\dfrac{2(x+3)}{(x+3)(x+2)(x+1)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{x^2+x-2x-6}{(x+3)(x+2)(x+1)}\\Rightarrow \\dfrac{x^2-x-6}{(x+3)(x+2)(x+1)}\\Rightarrow \\dfrac{(x-3)\\cancel{(x+2)}}{(x+3)\\cancel{(x+2)}(x+1)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{x-3}{(x+3)(x+1)}[\/latex]<\/li>\n
    14. [latex]\\text{LCD}=(x-1)(x+1)(x+4) \\hspace{0.25in} \\dfrac{2x(x+4)}{(x-1)(x+1)(x+4)}-\\dfrac{3(x-1)}{(x-1)(x+1)(x+4)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{2x^2+8x-3x+3}{(x-1)(x+1)(x+4)}\\Rightarrow \\dfrac{2x^2+5x+3}{(x-1)(x+1)(x+4)}\\Rightarrow \\dfrac{(2x+3)\\cancel{(x+1)}}{(x-1)\\cancel{(x+1)}(x+4)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{2x+3}{(x-1)(x+4)}[\/latex]<\/li>\n
    15. [latex]\\text{LCD}=(x+7)(x+8)(x+6) \\hspace{0.25in} \\dfrac{x(x+6)}{(x+7)(x+8)(x+6)}-\\dfrac{7(x+8)}{(x+7)(x+8)(x+6)}[\/latex]
      \n[latex]\\Rightarrow \\dfrac{x^2+6x-7x-56}{(x+7)(x+8)(x+6)}\\Rightarrow\\dfrac{x^2-x-56}{(x+7)(x+8)(x+6)}\\Rightarrow\\dfrac{(x-8)\\cancel{(x+7)}}{\\cancel{(x+7)}(x+8)(x+6)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{x-8}{(x+8)(x+6)}[\/latex]<\/li>\n
    16. [latex]\\text{LCD}=(x-3)(x+3)(x-2) \\hspace{0.25in} \\dfrac{2x(x-2)}{(x-3)(x+3)(x-2)}+\\dfrac{5(x-3)}{(x-3)(x+3)(x-2)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{2x^2-4x+5x-15}{(x-3)(x+3)(x-2)}\\Rightarrow \\dfrac{2x^2+x-15}{(x-3)(x+3)(x-2)}\\Rightarrow \\dfrac{\\cancel{(x+3)}(2x-5)}{(x-3)\\cancel{(x+3)}(x-2)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{2x-5}{(x-3)(x-2)}[\/latex]<\/li>\n
    17. [latex]\\text{LCD}=(x-3)(x+2)(x+3) \\hspace{0.25in} \\dfrac{5x(x+3)}{(x-3)(x+2)(x+3)}-\\dfrac{18(x+2)}{(x-3)(x+2)(x+3)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{5x^2+15x-18x-36}{(x-3)(x+2)(x+3)}\\Rightarrow \\dfrac{5x^2-3x-36}{(x-3)(x+2)(x+3)}\\Rightarrow \\dfrac{\\cancel{(x-3)}(5x+12)}{\\cancel{(x-3)}(x+2)(x+3)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{5x+12}{(x+2)(x+3)}[\/latex]<\/li>\n
    18. [latex]\\text{LCD}=(x-3)(x+1)(x-2) \\hspace{0.25in} \\dfrac{4x(x-2)}{(x-3)(x+1)(x-2)}-\\dfrac{3(x+1)}{(x-3)(x+1)(x-2)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{4x^2-8x-3x-3}{(x-3)(x+1)(x-2)}\\Rightarrow \\dfrac{4x^2-11x-3}{(x-3)(x+1)(x-2)}\\Rightarrow \\dfrac{(4x+1)\\cancel{(x-3)}}{\\cancel{(x-3)}(x+1)(x-2)}[\/latex]
      \n[latex]\\Rightarrow\\dfrac{4x+1}{(x+1)(x-2)}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":77,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1944","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1944","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1944\/revisions"}],"predecessor-version":[{"id":1945,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1944\/revisions\/1945"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1944\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1944"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1944"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1944"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1944"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}