{"id":1942,"date":"2021-12-02T19:40:06","date_gmt":"2021-12-03T00:40:06","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-3\/"},"modified":"2022-11-02T10:38:35","modified_gmt":"2022-11-02T14:38:35","slug":"answer-key-8-3","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-3\/","title":{"raw":"Answer Key 8.3","rendered":"Answer Key 8.3"},"content":{"raw":"
    \n \t
  1. [latex]12a^4b^5[\/latex]<\/li>\n \t
  2. [latex]25x^3y^5z[\/latex]<\/li>\n \t
  3. [latex]x(x-3)[\/latex]<\/li>\n \t
  4. [latex]4(x-2)[\/latex]<\/li>\n \t
  5. [latex](x+2)(x-4)[\/latex]<\/li>\n \t
  6. [latex]x(x-7)(x+1)[\/latex]<\/li>\n \t
  7. [latex](x+5)(x-5)[\/latex]<\/li>\n \t
  8. [latex](x+3)(x-3)^2[\/latex]<\/li>\n \t
  9. [latex](x+1)(x+2)(x+3)[\/latex]<\/li>\n \t
  10. [latex](x-5)(x-2)(x+3)[\/latex]<\/li>\n \t
  11. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&10a^3b^2 \\\\ \\\\\n\\dfrac{3a}{5b^2}\\cdot \\dfrac{2a^3}{2a^3} &\\Rightarrow &\\dfrac{6a^4}{10a^3b^2} \\\\ \\\\\n\\dfrac{2}{10a^3b}\\cdot \\dfrac{b}{b} &\\Rightarrow & \\dfrac{2b}{10a^3b^2}\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&(x-4)(x+2) \\\\ \\\\\n\\dfrac{3x}{(x-4)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{3x^2+6x}{(x-4)(x+2)} \\\\ \\\\\n\\dfrac{2}{(x+2)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow &\\dfrac{2x-8}{(x-4)(x+2)}\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&(x-3)(x+2) \\\\ \\\\\n\\dfrac{(x+2)}{(x-3)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{x^2+4x+4}{(x-3)(x+2)} \\\\ \\\\\n\\dfrac{(x-3)}{(x+2)}\\cdot \\dfrac{(x-3)}{(x-3)}&\\Rightarrow &\\dfrac{x^2-6x+9}{(x-3)(x+2)}\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&x(x-6) \\\\ \\\\\n\\dfrac{5}{x^2-6x}&\\Rightarrow &\\dfrac{5}{x(x-6)} \\\\ \\\\\n\\dfrac{2}{x}\\cdot \\dfrac{(x-6)}{(x-6)}&\\Rightarrow &\\dfrac{2x-12}{x(x-6)} \\\\ \\\\\n\\dfrac{-3}{(x-6)}\\cdot \\dfrac{x}{x}&\\Rightarrow & \\dfrac{-3x}{x(x-6)}\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&(x-4)^2(x+4) \\\\ \\\\\n\\dfrac{x}{x^2-16}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow &\\dfrac{x^2-4x}{(x-4)^2(x+4)} \\\\ \\\\\n\\dfrac{3x}{(x^2-8x+16)}\\cdot \\dfrac{(x+4)}{(x+4)}&\\Rightarrow &\\dfrac{3x^2+12}{(x-4)^2(x+4)}\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&(x-5)(x+2) \\\\ \\\\\n\\dfrac{5x+1}{x^2-3x-10}&\\Rightarrow &\\dfrac{5x+1}{(x-5)(x+2)} \\\\ \\\\\n\\dfrac{4}{(x-5)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{4x+8}{(x-5)(x+2)}\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&(x+6)^2(x-6) \\\\ \\\\\n\\dfrac{x+1}{x^2-36}\\cdot \\dfrac{(x+6)}{(x+6)}&\\Rightarrow &\\dfrac{x^2+7x+6}{(x+6)^2(x-6)} \\\\ \\\\\n\\dfrac{(2x+3)}{(x^2+12x+36)}\\cdot \\dfrac{(x-6)}{(x-6)}&\\Rightarrow &\\dfrac{2x^2-9x-18}{(x+6)^2(x-6)}\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&(x-4)(x+3)(x+1) \\\\ \\\\\n\\dfrac{(3x+1)}{(x^2-x-12)}\\cdot \\dfrac{(x+1)}{(x+1)}&\\Rightarrow & \\dfrac{3x^2+4x+1}{(x-4)(x+3)(x+1)} \\\\ \\\\\n\\dfrac{2x}{(x^2+4x+3)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow & \\dfrac{2x^2-8x}{(x-4)(x+3)(x+1)}\n\\end{array}[\/latex]<\/li>\n \t
  19. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&(x-3)(x+2) \\\\ \\\\\n\\dfrac{4x}{x^2-x-6}&\\Rightarrow &\\dfrac{4x}{(x-3)(x+2)} \\\\ \\\\\n\\dfrac{(x+2)}{(x-3)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{x^2+4x+4}{(x-3)(x+2)}\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]\\begin{array}[t]{rrl}\n\\text{LCD}&=&(x-4)(x-2)(x+5) \\\\ \\\\\n\\dfrac{3x}{x^2-6x+8}\\cdot \\dfrac{(x+5)}{(x+5)}&\\Rightarrow & \\dfrac{3x^2+15x}{(x-4)(x-2)(x+5)} \\\\ \\\\\n\\dfrac{(x-2)}{(x^2+x-20)}\\cdot \\dfrac{(x-2)}{(x-2)}&\\Rightarrow & \\dfrac{x^2-4x+4}{(x-4)(x-2)(x+5)} \\\\ \\\\\n\\dfrac{5}{(x^2+3x-10)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow & \\dfrac{5x-20}{(x-4)(x-2)(x+5)}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]12a^4b^5[\/latex]<\/li>\n
    2. [latex]25x^3y^5z[\/latex]<\/li>\n
    3. [latex]x(x-3)[\/latex]<\/li>\n
    4. [latex]4(x-2)[\/latex]<\/li>\n
    5. [latex](x+2)(x-4)[\/latex]<\/li>\n
    6. [latex]x(x-7)(x+1)[\/latex]<\/li>\n
    7. [latex](x+5)(x-5)[\/latex]<\/li>\n
    8. [latex](x+3)(x-3)^2[\/latex]<\/li>\n
    9. [latex](x+1)(x+2)(x+3)[\/latex]<\/li>\n
    10. [latex](x-5)(x-2)(x+3)[\/latex]<\/li>\n
    11. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&10a^3b^2 \\\\ \\\\ \\dfrac{3a}{5b^2}\\cdot \\dfrac{2a^3}{2a^3} &\\Rightarrow &\\dfrac{6a^4}{10a^3b^2} \\\\ \\\\ \\dfrac{2}{10a^3b}\\cdot \\dfrac{b}{b} &\\Rightarrow & \\dfrac{2b}{10a^3b^2} \\end{array}[\/latex]<\/li>\n
    12. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&(x-4)(x+2) \\\\ \\\\ \\dfrac{3x}{(x-4)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{3x^2+6x}{(x-4)(x+2)} \\\\ \\\\ \\dfrac{2}{(x+2)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow &\\dfrac{2x-8}{(x-4)(x+2)} \\end{array}[\/latex]<\/li>\n
    13. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&(x-3)(x+2) \\\\ \\\\ \\dfrac{(x+2)}{(x-3)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{x^2+4x+4}{(x-3)(x+2)} \\\\ \\\\ \\dfrac{(x-3)}{(x+2)}\\cdot \\dfrac{(x-3)}{(x-3)}&\\Rightarrow &\\dfrac{x^2-6x+9}{(x-3)(x+2)} \\end{array}[\/latex]<\/li>\n
    14. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&x(x-6) \\\\ \\\\ \\dfrac{5}{x^2-6x}&\\Rightarrow &\\dfrac{5}{x(x-6)} \\\\ \\\\ \\dfrac{2}{x}\\cdot \\dfrac{(x-6)}{(x-6)}&\\Rightarrow &\\dfrac{2x-12}{x(x-6)} \\\\ \\\\ \\dfrac{-3}{(x-6)}\\cdot \\dfrac{x}{x}&\\Rightarrow & \\dfrac{-3x}{x(x-6)} \\end{array}[\/latex]<\/li>\n
    15. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&(x-4)^2(x+4) \\\\ \\\\ \\dfrac{x}{x^2-16}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow &\\dfrac{x^2-4x}{(x-4)^2(x+4)} \\\\ \\\\ \\dfrac{3x}{(x^2-8x+16)}\\cdot \\dfrac{(x+4)}{(x+4)}&\\Rightarrow &\\dfrac{3x^2+12}{(x-4)^2(x+4)} \\end{array}[\/latex]<\/li>\n
    16. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&(x-5)(x+2) \\\\ \\\\ \\dfrac{5x+1}{x^2-3x-10}&\\Rightarrow &\\dfrac{5x+1}{(x-5)(x+2)} \\\\ \\\\ \\dfrac{4}{(x-5)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{4x+8}{(x-5)(x+2)} \\end{array}[\/latex]<\/li>\n
    17. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&(x+6)^2(x-6) \\\\ \\\\ \\dfrac{x+1}{x^2-36}\\cdot \\dfrac{(x+6)}{(x+6)}&\\Rightarrow &\\dfrac{x^2+7x+6}{(x+6)^2(x-6)} \\\\ \\\\ \\dfrac{(2x+3)}{(x^2+12x+36)}\\cdot \\dfrac{(x-6)}{(x-6)}&\\Rightarrow &\\dfrac{2x^2-9x-18}{(x+6)^2(x-6)} \\end{array}[\/latex]<\/li>\n
    18. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&(x-4)(x+3)(x+1) \\\\ \\\\ \\dfrac{(3x+1)}{(x^2-x-12)}\\cdot \\dfrac{(x+1)}{(x+1)}&\\Rightarrow & \\dfrac{3x^2+4x+1}{(x-4)(x+3)(x+1)} \\\\ \\\\ \\dfrac{2x}{(x^2+4x+3)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow & \\dfrac{2x^2-8x}{(x-4)(x+3)(x+1)} \\end{array}[\/latex]<\/li>\n
    19. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&(x-3)(x+2) \\\\ \\\\ \\dfrac{4x}{x^2-x-6}&\\Rightarrow &\\dfrac{4x}{(x-3)(x+2)} \\\\ \\\\ \\dfrac{(x+2)}{(x-3)}\\cdot \\dfrac{(x+2)}{(x+2)}&\\Rightarrow &\\dfrac{x^2+4x+4}{(x-3)(x+2)} \\end{array}[\/latex]<\/li>\n
    20. [latex]\\begin{array}[t]{rrl} \\text{LCD}&=&(x-4)(x-2)(x+5) \\\\ \\\\ \\dfrac{3x}{x^2-6x+8}\\cdot \\dfrac{(x+5)}{(x+5)}&\\Rightarrow & \\dfrac{3x^2+15x}{(x-4)(x-2)(x+5)} \\\\ \\\\ \\dfrac{(x-2)}{(x^2+x-20)}\\cdot \\dfrac{(x-2)}{(x-2)}&\\Rightarrow & \\dfrac{x^2-4x+4}{(x-4)(x-2)(x+5)} \\\\ \\\\ \\dfrac{5}{(x^2+3x-10)}\\cdot \\dfrac{(x-4)}{(x-4)}&\\Rightarrow & \\dfrac{5x-20}{(x-4)(x-2)(x+5)} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":76,"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-1942","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\/1942","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\/1942\/revisions"}],"predecessor-version":[{"id":1943,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1942\/revisions\/1943"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1942\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1942"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1942"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1942"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}