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5.6E: Exercises

  • Page ID
    104864
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    Solve Rational Equations

    In the following exercises, solve each rational equation.

    Solve Rational Equations

    Solve the following

    1. \(\dfrac{1}{a}+\dfrac{2}{5}=\dfrac{1}{2}\)
    2. \(\dfrac{4}{5}+\dfrac{1}{4}=\dfrac{2}{v}\)
    3. \(1-\dfrac{2}{m}=\dfrac{8}{m^{2}}\)
    4. \(1+\dfrac{9}{p}=\dfrac{-20}{p^{2}}\)
    5. \(\dfrac{5}{3 v-2}=\dfrac{7}{4 v}\)
    6. \(\dfrac{3}{x+4}+\dfrac{7}{x-4}=\dfrac{8}{x^{2}-16}\)
    7. \(\dfrac{8}{z-10}-\dfrac{7}{z+10}=\dfrac{5}{z^{2}-100}\)
    8. \(\dfrac{-10}{q-2}-\dfrac{7}{q+4}=1\)
    9. \(\dfrac{v-10}{v^{2}-5 v+4}=\dfrac{3}{v-1}-\dfrac{6}{v-4}\)
    10. \(\dfrac{x-10}{x^{2}+8 x+12}=\dfrac{3}{x+2}+\dfrac{4}{x+6}\)
    11. \(\dfrac{b+3}{3 b}+\dfrac{b}{24}=\dfrac{1}{b}\)
    12. \(\dfrac{d}{d+3}=\dfrac{18}{d^{2}-9}+4\)
    13. \(\dfrac{n}{n+2}-3=\dfrac{8}{n^{2}-4}\)
    14. \(\dfrac{q}{3 q-9}-\dfrac{3}{4 q+12}=\dfrac{7 q^{2}+6 q+63}{24 q^{2}-216}\)
    15. \(\dfrac{s}{2 s+6}-\dfrac{2}{5 s+5}=\dfrac{5 s^{2}-3 s-7}{10 s^{2}+40 s+30}\)
    16. \(\dfrac{2}{x^{2}+2 x-8}-\dfrac{1}{x^{2}+9 x+20}=\dfrac{4}{x^{2}+3 x-10}\)
    17. \(\dfrac{3}{x^{2}-5 x-6}+\dfrac{3}{x^{2}-7 x+6}=\dfrac{6}{x^{2}-1}\)
    Answer
    1. \(a=10\)
    2. \(v=\dfrac{40}{21}\)
    3. \(m=-2,\; m=4\)
    4. \(p=-5, \; p=-4\)
    5. \(v=14\)
    6. \(x=-\dfrac{4}{5}\)
    7. \(z=-145\)
    8. \(q=-18, \; q=-1\)
    9. no solution
    10. no solution
    11. \(b=-8\)
    12. \(d=2\)
    13. \(n=1\)
    14. no solution
    15. \(s=\dfrac{5}{4}\)
    16. \(x=-\dfrac{4}{3}\)
    17. no solution

    Writing Exercises

    1. Your class mate is having trouble in this section. Write down the steps you would use to explain how to solve a rational equation.
    2. Alek thinks the equation \(\dfrac{y}{y+6}=\dfrac{72}{y^{2}-36}+4\) has two solutions, \(y=-6\) and \(y=4\). Explain why Alek is wrong.
    Answer

    Answers will vary.


    This page titled 5.6E: Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Stanislav A. Trunov and Elizabeth J. Hale via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.