{"id":1641,"date":"2019-07-30T14:40:00","date_gmt":"2019-07-30T18:40:00","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1641"},"modified":"2019-07-30T16:25:17","modified_gmt":"2019-07-30T20:25:17","slug":"answer-key-8-4","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-8-4\/","title":{"raw":"Answer Key 8.4","rendered":"Answer Key 8.4"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\dfrac{2+4}{a+3}=\\dfrac{6}{a+3}\\)<\/li>\r\n \t
  2. \\(\\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\\)<\/li>\r\n \t
  3. \\(\\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\\)<\/li>\r\n \t
  4. \\(\\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}\\)<\/li>\r\n \t
  5. \\(\\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}\\)<\/li>\r\n \t
  6. \\(\\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}\\)<\/li>\r\n \t
  7. \\(\\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}\\)<\/li>\r\n \t
  8. \\(\\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}\\)<\/li>\r\n \t
  9. \\(\\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}\\)<\/li>\r\n \t
  10. \\(\\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}\\)<\/li>\r\n \t
  11. \\(\\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\\)\r\n\\(\\dfrac{3y^2-3xy-6x^2}{2x^2y^2}\\)<\/li>\r\n \t
  12. \\(\\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\\)\r\n\\(\\dfrac{4x}{(x+1)(x-1)}\\)<\/li>\r\n \t
  13. \\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{x-3}{(x+3)(x+1)}\\)<\/li>\r\n \t
  14. \\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{2x+3}{(x-1)(x+4)}\\)<\/li>\r\n \t
  15. \\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{x-8}{(x+8)(x+6)}\\)<\/li>\r\n \t
  16. \\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{2x-5}{(x-3)(x-2)}\\)<\/li>\r\n \t
  17. \\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{5x+12}{(x+2)(x+3)}\\)<\/li>\r\n \t
  18. \\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\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)}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{4x+1}{(x+1)(x-2)}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\dfrac{2+4}{a+3}=\dfrac{6}{a+3}\"<\/li>\n
    2. \"\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\"<\/li>\n
    3. \"\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\"<\/li>\n
    4. \"\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}\"<\/li>\n
    5. \"\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}\"<\/li>\n
    6. \"\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}\"<\/li>\n
    7. \"\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}\"<\/li>\n
    8. \"\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}\"<\/li>\n
    9. \"\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}\"<\/li>\n
    10. \"\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}\"<\/li>\n
    11. \"\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\"
      \n\"\dfrac{3y^2-3xy-6x^2}{2x^2y^2}\"<\/li>\n
    12. \"\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\"
      \n\"\dfrac{4x}{(x+1)(x-1)}\"<\/li>\n
    13. \"\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)}\Rightarrow \\\"
      \n\"\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)}\Rightarrow \\\"
      \n\"\dfrac{x-3}{(x+3)(x+1)}\"<\/li>\n
    14. \"\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)}\Rightarrow \\\"
      \n\"\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)}\Rightarrow \\\"
      \n\"\dfrac{2x+3}{(x-1)(x+4)}\"<\/li>\n
    15. \"\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)}\Rightarrow \\\"
      \n\"\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)}\Rightarrow \\\"
      \n\"\dfrac{x-8}{(x+8)(x+6)}\"<\/li>\n
    16. \"\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)}\Rightarrow \\\"
      \n\"\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)}\Rightarrow \\\"
      \n\"\dfrac{2x-5}{(x-3)(x-2)}\"<\/li>\n
    17. \"\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)}\Rightarrow \\\"
      \n\"\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)}\Rightarrow \\\"
      \n\"\dfrac{5x+12}{(x+2)(x+3)}\"<\/li>\n
    18. \"\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)}\Rightarrow \\\"
      \n\"\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)}\Rightarrow \\\"
      \n\"\dfrac{4x+1}{(x+1)(x-2)}\"<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":72,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1641","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1641","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1641\/revisions"}],"predecessor-version":[{"id":1645,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1641\/revisions\/1645"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1641\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1641"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1641"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1641"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}