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5.5E: Exercises

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    Practice Makes Perfect

    Add and Subtract with Common Denominator

    In the following exercises, add or subtract.

    1. \(\dfrac{2}{15}+\dfrac{7}{15}\)
    2. \(\dfrac{3c}{4c−5}+\dfrac{5}{4c−5}\)
    3. \(\dfrac{2r^2}{2r−1}+\dfrac{15r−8}{2r−1}\)
    4. \(\dfrac{2w^2}{w^2−16}+\dfrac{8w}{w^2−16}\)
    5. \(\dfrac{9a^2}{3a−7}−\dfrac{49}{3a−7}\)
    6. \(\dfrac{3m^2}{6m−30}−\dfrac{21m−30}{6m−30}\)
    7. \(\dfrac{6p^2+3p+4}{p^2+4p−5}−\dfrac{5p^2+p+7}{p^2+4p−5}\)
    8. \(\dfrac{5r^2+7r−33}{r^2−49}−\dfrac{4r^2+5r+30}{r^2−49}\)
    Answer
    1. \(\dfrac{3}{5}\)
    2. \(\dfrac{3c+5}{4c−5}\)
    3. \(r+8\)
    4. \(\dfrac{2w}{w−4}\)
    5. \(3a+7\)
    6. \(\dfrac{m−2}{2}\)
    7. \(\dfrac{p+3}{p+5}\)
    8. \(\dfrac{r+9}{r+7}\)
    Add and Subtract with Opposite Denominators

    In the following exercises, add or subtract.

    1. \(\dfrac{10v}{2v−1}+\dfrac{2v+4}{1−2v}\)
    2. \(\dfrac{10x^2+16x−7}{8x−3}+\dfrac{2x^2+3x−1}{3−8x}\)
    3. \(\dfrac{z^2+6z}{z^2−25}−\dfrac{3z+20}{25−z^2}\)
    4. \(\dfrac{2b^2+30b−13}{b^2−49}−\dfrac{2b^2−5b−8}{49−b^2}\)
    Answer
    1. \(4\)
    2. \(x+2\)
    3. \(\dfrac{z+4}{z−5}\)
    4. \(\dfrac{4b−3}{b−7}\)
    Add and Subtract with Unlike Denominators.

    In the following exercises, perform the indicated operations.

    1. \(\dfrac{7}{10x^2y}+\dfrac{4}{15xy^2}\)
    2. \(\dfrac{3}{r+4}+\dfrac{2}{r−5}\)
    3. \(\dfrac{5}{3w−2}+\dfrac{2}{w+1}\)
    4. \(\dfrac{2y}{y+3}+\dfrac{3}{y−1}\)
    5. \(\dfrac{5b}{a^2b−2a^2}+\dfrac{2b}{b^2−4}\)
    6. \(\dfrac{−3m}{3m−3}+\dfrac{5m}{m^2+3m−4}\)
    7. \(\dfrac{3r}{r^2+7r+6}+\dfrac{9}{r^2+4r+3}\)
    8. \(\dfrac{t}{t−6}−\dfrac{t−2}{t+6}\)
    9. \(\dfrac{5a}{a+3}−\dfrac{a+2}{a+6}\)
    10. \(\dfrac{6}{m+6}−\dfrac{12m}{m^2−36}\)
    11. \(\dfrac{−9p−17}{p^2−4p−21}−\dfrac{p+1}{7−p}\)
    12. \(\dfrac{−2r−16}{r^2+6r−16}−\dfrac{5}{2−r}\)
    13. \(\dfrac{2x+7}{10x−1}+3\)
    14. \(\dfrac{3}{x^2−3x−4}−\dfrac{2}{x^2−5x+4}\)
    15. \(\dfrac{5}{x^2+8x−9}−\dfrac{4}{x^2+10x+9}\)
    16. \(\dfrac{5a}{a−2}+\dfrac{9}{a}−\dfrac{2a+18}{a^2−2a}\)
    17. \(\dfrac{c}{c+2}+\dfrac{5}{c−2}−\dfrac{10c}{c^2−4}\)
    18. \(\dfrac{3d}{d+2}+\dfrac{4}{d}−\dfrac{d+8}{d^2+2d}\)
    Answer
    1. \(\dfrac{21y+8x}{30x^2y^2}\)
    2. \(\dfrac{5r−7}{(r+4)(r−5)}\)
    3. \(\dfrac{11w+1}{(3w−2)(w+1)}\)
    4. \(\dfrac{2y^2+y+9}{(y+3)(y−1)}\)
    5. \(\dfrac{b(5b+10+2a^2)}{a^2(b−2)(b+2)}\)
    6. \(-\dfrac{m}{m+4}\)
    7. \(\dfrac{3(r^2+6r+18)}{(r+1)(r+6)(r+3)}\)
    8. \(\dfrac{2(7t−6)}{(t−6)(t+6)}\)
    9. \(\dfrac{4a^2+25a−6}{(a+3)(a+6)}\)
    10. \(\dfrac{−6}{m−6}\)
    11. \(\dfrac{p+2}{p+3}\)
    12. \(\dfrac{3}{r−2}\)
    13. \(\dfrac{4(8x+1)}{10x−1}\)
    14. \(\dfrac{x−5}{(x−4)(x+1)(x−1)}\)
    15. \(\dfrac{1}{(x−1)(x+1)}\)
    16. \(\dfrac{5a^2+7a−36}{a(a−2)}\)
    17. \(\dfrac{c−5}{c+2}\)
    18. \(\dfrac{3(d+1)}{d+2}\)
    Writing Exercises
    1. Donald thinks that \(\dfrac{3}{x}+\dfrac{4}{x}\) is \(\dfrac{7}{2x}\). Is Donald correct? Explain.
    2. Explain how you find the Least Common Denominator of \(x^2+5x+4\) and \(x^2−16\).
    3. Simplify the expression \(\dfrac{4}{n^2+6n+9}−\dfrac{1}{n^2−9}\) and explain all your steps.
    Answer

    Answers will vary

    This page titled 5.5E: 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.