Honors Algebra 2: Extra Practice on Adding and Subtracting Rational Expressions

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  1. \( \displaystyle \frac{ 5x}{8} + \frac{3x}{2} + \frac{ x }{ 4 } \)
    2. Solution

    \( \displaystyle \frac{ 19x}{ 8} \)

  2. \( \displaystyle \frac{ 3m}{7} + \frac{ m }{ 14 } + \frac{ 5m }{ 2 } \)
    3. Solution

    \( \displaystyle 3m\)

  3. \( \displaystyle \frac{ 3x - 5 }{ 6 } + \frac{ 2x + 1 }{ 4 }\)
    4. Solution

    \( \displaystyle \frac{ 12x - 7}{ 12} \)

  4. \( \displaystyle \frac{ 4y - 1 }{ 5 } + \frac{ y }{ 10 } + \frac{ 3y - 2 }{ 6 } \)
    5. Solution

    \( \displaystyle \frac{ 21y - 8}{ 15} \)

  5. \( \displaystyle \left( \frac{ 2a }{ 3 } + \frac{ 1 }{ 6 } \right) \div \frac{ 16a^2 - 1 }{ 12 }\)
    6. Solution

    \( \displaystyle \frac{ 2}{ 4a - 1} \)

  6. \( \displaystyle \frac{ 3x - 2 }{ x^2 - 5x } + \frac{ 4 }{ x^2 - 7x + 10 } \)
    7. Solution

    \( \displaystyle \frac{ 3x^2 - 4x + 4}{ x(x - 5)(x - 2)} \)

  7. \( \displaystyle \frac{ 6k - 22 }{ k^2 - 5k + 6 } +\frac{ k + 1 }{ k - 3 }\)
    8. Solution

    \( \displaystyle \frac{ k + 8}{ k - 2} , k \ne 3 \)

  8. \( \displaystyle \frac{ 5 }{ a } + 6 \)
    9. Solution

    \( \displaystyle \frac{ 6a + 5}{ a} \)

  9. \( \displaystyle 9 + \frac{ 4 }{ m } \)
    10. Solution

    \( \displaystyle \frac{ 9m + 4}{ m} \)

  10. \( \displaystyle \frac{ 7 }{ a - 3 } + \frac{ 4 }{ a + 6 }\)
    11. Solution

    \( \displaystyle \frac{ 11a + 30}{ (a - 3)(a + 6)} \)

  11. \( \displaystyle \frac{ 3 }{ b - 4 }+ \frac{ 2 }{ b + 5 }\)
    12. Solution

    \( \displaystyle \frac{ 5b + 7}{ (b - 4)(b + 5)} \)

  12. \( \displaystyle \frac{ 7 }{ 2a } + \frac{ 2a }{ 3a^2 } + \frac{ 3+5a }{ 6a^3 } \)
    13. Solution

    \( \displaystyle \frac{ 19a^2 + 9a + 3}{ 6a^3} \)

  13. \( \displaystyle x - 5 + \frac{ 7 }{ 3x + 2 } \)
    14. Solution

    \( \displaystyle \frac{ 3x^2 - 13x - 3}{ 3x + 2}\)

  14. \( \displaystyle \frac{ 4 }{ a - 2 } + \frac{ 3 }{ a - 1 } + \frac{ 2}{ a + 1 } \)
    15. Solution

    \( \displaystyle \frac{ 9a^2 - 9a - 6}{ (a - 2)(a - 1)(a + 1)} \)

  15. \( \displaystyle \frac{ 6 }{ x - 5 }- \frac{ x - 3 }{ x^2 - 25 } \)
    16. Solution

    \( \displaystyle \frac{ 5x + 33}{ (x + 5)(x - 5)} \)

  16. \( \displaystyle \frac{ 5 }{ 3b - 2 } - \frac{ 4 }{ 2b + 5 }\)
    17. Solution

    \( \displaystyle \frac{ -2b + 33}{ (3b - 2)(2b + 5)} \)

  17. \( \displaystyle \frac{ 7 }{ 12y^3 } - \frac{ 3 }{ 8y^2 } \)
    18. Solution

    \( \displaystyle \frac{ 14 - 9y}{ 24y^3} \)

  18. \( \displaystyle \frac{ 2 }{ 9m^2 }- \frac{ 5 }{ 3m } \)
    19. Solution

    \( \displaystyle \frac{ 2 - 15m}{ 9m^2} \)

  19. \( \displaystyle \frac{ 5 }{ k^2 - 5k - 24 } - \frac{ 2 }{ k - 8 }\)

    20. Solution

    \( \displaystyle -\frac{ 2x + 1)}{ (k - 8)(x + 3)} \)

  20. \( \displaystyle \frac{ 5 }{ k^2 - 5k - 14 } - \frac{k - 1}{k - 7} \)
    21. Solution

    \( \displaystyle -\frac{ k^2 + k - 7}{ (k - 7)(k + 2)} \)

  21. \( \displaystyle \frac{ 4 }{ xy - 3x + ay - 3a } - \frac{ a + 1 }{ y^2 + y - 12 } \)
    22. Solution

    \( \displaystyle \frac{ 4y + 16 - xa - x - a^2 - a}{ (x + a)(y - 3)(y + 4)} \)

  22. \( \displaystyle \frac{ 3 }{ xy - 3xb + 2y^2 - 6yb }- \frac{ 7 }{ y^2 - 9b^2 } \)
    23. Solution

    \( \displaystyle \frac{ -11y+9b-7k}{ (x + 2y)(y - 3b)(y + 3b)} \)

  23. \( \displaystyle \frac{ 4a }{ a^2 - 9 } + \frac{2}{3 - a}\)
    24. Solution

    \( \displaystyle \frac{ 2}{ a + 3} , a \ne 3 \)

  24. \( \displaystyle \frac{ 5y + 2 }{ y^2 - 4y - 12 } + \frac{ 4 }{ 6 - y } \)
    25. Solution

    \( \displaystyle \frac{ 1}{ y + 2} , y \ne 6 \)

  25. \( \displaystyle \frac{ 18 - 17b }{ b^2 + 2b - 48 } - \frac{ b }{ 6 - b } \)
    26. Solution

    \( \displaystyle \frac{ b - 3}{ b + 8} , b \ne 6 \)

  26. \( \displaystyle \frac{ 4 }{ m - 8 } + \frac{ 3 }{ 4 - m } \)
    27. Solution

    \( \displaystyle \frac{ m + 8}{ (m - 8)(m - 4)} \)

  27. \( \displaystyle \frac{ 3 }{ t } - \frac{ 7 - t }{ 2t - t^2 } \)
    28. Solution

    \( \displaystyle \frac{ 2t + 1}{ t(t - 2)} \)

  28. \( \displaystyle \frac{ 9y - 22 }{ y^2 - 2y } - \frac{ y }{ 2 - y } \)
    29. Solution

    \( \displaystyle \frac{ y + 11}{ y}, y \ne 2 \)