{"id":1648,"date":"2019-07-30T16:53:08","date_gmt":"2019-07-30T20:53:08","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1648"},"modified":"2020-02-03T13:55:50","modified_gmt":"2020-02-03T18:55:50","slug":"answer-key-8-5","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-8-5\/","title":{"raw":"Answer Key 8.5","rendered":"Answer Key 8.5"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\dfrac{\\left(1+\\dfrac{1}{x}\\right)x^2}{\\left(1-\\dfrac{1}{x^2}\\right)x^2}\\Rightarrow \\dfrac{x^2+x}{x^2-1}\\Rightarrow \\dfrac{x\\cancel{(x+1)}}{\\cancel{(x+1)}(x-1)}\\Rightarrow \\dfrac{x}{x-1}\\)<\/li>\r\n \t
  2. \\(\\dfrac{\\left(1-\\dfrac{1}{y^2}\\right)y^2}{\\left(1+\\dfrac{1}{y}\\right)y^2}\\Rightarrow \\dfrac{y^2-1}{y^2+y}\\Rightarrow \\dfrac{(y-1)\\cancel{(y+1)}}{y\\cancel{(y+1)}}\\Rightarrow \\dfrac{y-1}{y}\\)<\/li>\r\n \t
  3. \\(\\dfrac{\\left(\\dfrac{a}{b}+2\\right)b^2}{\\left(\\dfrac{a^2}{b^2}-4\\right)b^2}\\Rightarrow \\dfrac{ab+2b^2}{a^2-4b^2}\\Rightarrow \\dfrac{b\\cancel{(a+2b)}}{\\cancel{(a+2b)}(a-2b)}\\Rightarrow \\dfrac{b}{a-2b}\\)<\/li>\r\n \t
  4. \\(\\dfrac{\\left(\\dfrac{1}{y^2}-9\\right)y^2}{\\left(\\dfrac{1}{y}+3\\right)y^2}\\Rightarrow \\dfrac{1-9y^2}{y+3y^2}\\Rightarrow \\dfrac{(1-3y)\\cancel{(1+3y)}}{y\\cancel{(1+3y)}}\\Rightarrow \\dfrac{1-3y}{y}\\)<\/li>\r\n \t
  5. \\(\\dfrac{\\left(\\dfrac{1}{a^2}-\\dfrac{1}{a}\\right)a^2}{\\left(\\dfrac{1}{a^2}+\\dfrac{1}{a}\\right)a^2}\\Rightarrow \\dfrac{1-a}{1+a}\\)<\/li>\r\n \t
  6. \\(\\dfrac{\\left(\\dfrac{1}{b}+\\dfrac{1}{2}\\right)2b(b^2-1)}{\\left(\\dfrac{4}{b^2-1}\\right)2b(b^2-1)}\\Rightarrow \\dfrac{2b(b^2-1)+b(b^2-1)}{4(2b)}\\Rightarrow \\dfrac{2b^2-2+b^3-b}{8b}\\Rightarrow \\\\ \\\\ \\)\r\n\\(\\dfrac{b^3+2b^2-b-2}{8b}\\Rightarrow \\dfrac{(b-1)(b+1)(b+2)}{8b}\\)<\/li>\r\n \t
  7. \\(\\dfrac{\\left(x+2-\\dfrac{9}{x+2}\\right)(x+2)}{\\left(x+1+\\dfrac{x-7}{x+2}\\right)(x+2)}\\Rightarrow \\dfrac{(x+2)(x+2)-9}{(x+1)(x+2)+x-7}\\Rightarrow \\dfrac{x^2+4x+4-9}{x^2+3x+2+x-7}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{x^2+4x-5}{x^2+4x-5}\\Rightarrow 1\\)<\/li>\r\n \t
  8. \\(\\dfrac{\\left(a-3+\\dfrac{a-3}{a+2}\\right)(a+2)}{\\left(a+4-\\dfrac{4a+5}{a+2}\\right)(a+2)}\\Rightarrow \\dfrac{(a-3)(a+2)+a-3}{(a+4)(a+2)-4a+5}\\Rightarrow \\dfrac{a^2-a-6+a-3}{a^2+6a+8-4a+5}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{a^2-9}{a^2+2a+13}\\Rightarrow \\dfrac{(a-3)(a+3)}{a^2+2a+13}\\)<\/li>\r\n \t
  9. \\(\\dfrac{\\left(\\dfrac{x+y}{y}+\\dfrac{y}{x-y}\\right)y(x-y)}{\\left(\\dfrac{y}{x-y}\\right)y(x-y)}\\Rightarrow \\dfrac{(x+y)(x-y)+y(y)}{y(y)}\\Rightarrow \\\\ \\\\ \\)\r\n\\(\\dfrac{x^2-y^2+y^2}{y^2}\u00a0 \\Rightarrow \\dfrac{x^2}{y^2}\\)<\/li>\r\n \t
  10. \\(\\dfrac{\\left(\\dfrac{a-b}{a}-\\dfrac{a}{a+b}\\right)a(a+b)}{\\left(\\dfrac{b^2}{a+b}\\right)a(a+b)}\\Rightarrow \\dfrac{(a-b)(a+b)-a(a)}{b^2(a)}\\Rightarrow \\\\ \\\\ \\)\r\n\\(\\dfrac{a^2-b^2-a^2}{ab^2}\\Rightarrow \\dfrac{-b^2}{ab^2}\\)<\/li>\r\n \t
  11. \\(\\dfrac{\\left(\\dfrac{x-y}{y}+\\dfrac{x+y}{x-y}\\right)y(x-y)}{\\left(\\dfrac{y}{x-y}\\right)y(x-y)}\\Rightarrow \\dfrac{(x-y)(x-y)+(x+y)(y)}{y(y)}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{x^2-2xy+y^2+xy+y^2}{y^2}\\Rightarrow \\dfrac{x^2-xy+2y^2}{y^2}\\)<\/li>\r\n \t
  12. \\(\\dfrac{\\left(\\dfrac{x-2}{x+2}-\\dfrac{x+2}{x-2}\\right)(x+2)(x-2)}{\\left(\\dfrac{x-2}{x+2}+\\dfrac{x+2}{x-2}\\right)(x+2)(x-2)}\\Rightarrow \\dfrac{x^2-4x+4-(x^2+4x+4)}{x^2-4x+4+x^2+4x+4}\\Rightarrow \\dfrac{-8x}{2x^2+8}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{\\cancel{2}(-4x)}{\\cancel{2}(x^2+4)}\\Rightarrow \\dfrac{-4x}{x^2+4}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\dfrac{\left(1+\dfrac{1}{x}\right)x^2}{\left(1-\dfrac{1}{x^2}\right)x^2}\Rightarrow \dfrac{x^2+x}{x^2-1}\Rightarrow \dfrac{x\cancel{(x+1)}}{\cancel{(x+1)}(x-1)}\Rightarrow \dfrac{x}{x-1}\"<\/li>\n
    2. \"\dfrac{\left(1-\dfrac{1}{y^2}\right)y^2}{\left(1+\dfrac{1}{y}\right)y^2}\Rightarrow \dfrac{y^2-1}{y^2+y}\Rightarrow \dfrac{(y-1)\cancel{(y+1)}}{y\cancel{(y+1)}}\Rightarrow \dfrac{y-1}{y}\"<\/li>\n
    3. \"\dfrac{\left(\dfrac{a}{b}+2\right)b^2}{\left(\dfrac{a^2}{b^2}-4\right)b^2}\Rightarrow \dfrac{ab+2b^2}{a^2-4b^2}\Rightarrow \dfrac{b\cancel{(a+2b)}}{\cancel{(a+2b)}(a-2b)}\Rightarrow \dfrac{b}{a-2b}\"<\/li>\n
    4. \"\dfrac{\left(\dfrac{1}{y^2}-9\right)y^2}{\left(\dfrac{1}{y}+3\right)y^2}\Rightarrow \dfrac{1-9y^2}{y+3y^2}\Rightarrow \dfrac{(1-3y)\cancel{(1+3y)}}{y\cancel{(1+3y)}}\Rightarrow \dfrac{1-3y}{y}\"<\/li>\n
    5. \"\dfrac{\left(\dfrac{1}{a^2}-\dfrac{1}{a}\right)a^2}{\left(\dfrac{1}{a^2}+\dfrac{1}{a}\right)a^2}\Rightarrow \dfrac{1-a}{1+a}\"<\/li>\n
    6. \"\dfrac{\left(\dfrac{1}{b}+\dfrac{1}{2}\right)2b(b^2-1)}{\left(\dfrac{4}{b^2-1}\right)2b(b^2-1)}\Rightarrow \dfrac{2b(b^2-1)+b(b^2-1)}{4(2b)}\Rightarrow \dfrac{2b^2-2+b^3-b}{8b}\Rightarrow \\ \\\"
      \n\"\dfrac{b^3+2b^2-b-2}{8b}\Rightarrow \dfrac{(b-1)(b+1)(b+2)}{8b}\"<\/li>\n
    7. \"\dfrac{\left(x+2-\dfrac{9}{x+2}\right)(x+2)}{\left(x+1+\dfrac{x-7}{x+2}\right)(x+2)}\Rightarrow \dfrac{(x+2)(x+2)-9}{(x+1)(x+2)+x-7}\Rightarrow \dfrac{x^2+4x+4-9}{x^2+3x+2+x-7}\Rightarrow \\\"
      \n\"\dfrac{x^2+4x-5}{x^2+4x-5}\Rightarrow 1\"<\/li>\n
    8. \"\dfrac{\left(a-3+\dfrac{a-3}{a+2}\right)(a+2)}{\left(a+4-\dfrac{4a+5}{a+2}\right)(a+2)}\Rightarrow \dfrac{(a-3)(a+2)+a-3}{(a+4)(a+2)-4a+5}\Rightarrow \dfrac{a^2-a-6+a-3}{a^2+6a+8-4a+5}\Rightarrow \\\"
      \n\"\dfrac{a^2-9}{a^2+2a+13}\Rightarrow \dfrac{(a-3)(a+3)}{a^2+2a+13}\"<\/li>\n
    9. \"\dfrac{\left(\dfrac{x+y}{y}+\dfrac{y}{x-y}\right)y(x-y)}{\left(\dfrac{y}{x-y}\right)y(x-y)}\Rightarrow \dfrac{(x+y)(x-y)+y(y)}{y(y)}\Rightarrow \\ \\\"
      \n\"\dfrac{x^2-y^2+y^2}{y^2} \Rightarrow \dfrac{x^2}{y^2}\"<\/li>\n
    10. \"\dfrac{\left(\dfrac{a-b}{a}-\dfrac{a}{a+b}\right)a(a+b)}{\left(\dfrac{b^2}{a+b}\right)a(a+b)}\Rightarrow \dfrac{(a-b)(a+b)-a(a)}{b^2(a)}\Rightarrow \\ \\\"
      \n\"\dfrac{a^2-b^2-a^2}{ab^2}\Rightarrow \dfrac{-b^2}{ab^2}\"<\/li>\n
    11. \"\dfrac{\left(\dfrac{x-y}{y}+\dfrac{x+y}{x-y}\right)y(x-y)}{\left(\dfrac{y}{x-y}\right)y(x-y)}\Rightarrow \dfrac{(x-y)(x-y)+(x+y)(y)}{y(y)}\Rightarrow \\\"
      \n\"\dfrac{x^2-2xy+y^2+xy+y^2}{y^2}\Rightarrow \dfrac{x^2-xy+2y^2}{y^2}\"<\/li>\n
    12. \"\dfrac{\left(\dfrac{x-2}{x+2}-\dfrac{x+2}{x-2}\right)(x+2)(x-2)}{\left(\dfrac{x-2}{x+2}+\dfrac{x+2}{x-2}\right)(x+2)(x-2)}\Rightarrow \dfrac{x^2-4x+4-(x^2+4x+4)}{x^2-4x+4+x^2+4x+4}\Rightarrow \dfrac{-8x}{2x^2+8}\Rightarrow \\\"
      \n\"\dfrac{\cancel{2}(-4x)}{\cancel{2}(x^2+4)}\Rightarrow \dfrac{-4x}{x^2+4}\"<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":73,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1648","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1648","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":5,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1648\/revisions"}],"predecessor-version":[{"id":3787,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1648\/revisions\/3787"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1648\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1648"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1648"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1648"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}