Honors Algebra 2: Extra Practice on Compound Fractions



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  1. \( \displaystyle \frac{ 3a + \displaystyle \frac{ 1 }{ 5 } }{ \displaystyle \frac{ a }{ 2 } + \frac{ 7 }{ 10 }}\)
  2. Solution

    \( \displaystyle \frac{30a + 2}{5a + 7}\)

  3. \( \displaystyle \frac{ \displaystyle \frac{ 7 }{ y^2 } - \frac{ 2 }{ y } }{ \displaystyle \frac{ 13 }{ y } + \frac{ 1 }{ y^2 } } \)
  4. Solution

    \( \displaystyle \frac{7 - 2y}{13y + 1}; y \ne 0\)

  5. \( \displaystyle \frac{ 1 - \displaystyle \frac{ 11 }{ a } + \frac{ 28 }{ a^2 } }{ \displaystyle \frac{ 1 }{ a } - \frac{ 4 }{ a^2 } } \)
  6. Solution

    \(a - 7; a \ne 0\)

  7. \( \displaystyle \frac{ 1 - \displaystyle \frac{ 41 }{ m^2 } + \frac{ 400 }{ m^4 } }{ \displaystyle \frac{ 20 }{ m^4 } + \frac{ 1 }{ m^3 } - \frac{ 1 }{ m^2 } } \)
  8. Solution

    \( -(m + 5)(m - 4); m \ne 0\)

  9. \( \displaystyle \frac{ \displaystyle \frac{ a }{ a^2 - 7a + 10 } + \frac{ 2 }{ a - 5 } }{ \displaystyle \frac{ 4 }{ a - 5 } + \frac{ 2 }{ a - 2 } } \)
  10. Solution

    \( \displaystyle \frac{3a - 4}{6a - 18}, a \ne 5, 2\)

  11. \( \displaystyle \frac{ \displaystyle \frac{ 7 }{ x^2 - 7x + 12 } + \frac{ 3 }{ x - 4 } }{ \displaystyle \frac{ 2 }{ x - 4 } + \frac{ 7 }{ x - 3 } } \)
  12. Solution

    \( \displaystyle \frac{3x - 2}{9x - 34}; x \ne 3, 4\)

  13. \( \displaystyle \frac{ m + 2 + \displaystyle \frac{ 3 }{ m - 5 } }{ \displaystyle \frac{ 4 }{ m - 5 } + 1 } \)
  14. Solution

    \( \displaystyle \frac{m^2 - 3m - 7}{m - 1}; m \ne 5\)

  15. \( \displaystyle \frac{ \displaystyle \frac{ 4 }{ m + 5 } - \frac{ 20 }{ m^2 + 5m } }{ \displaystyle \frac{ 2 }{ m + 5 } - \frac{ 1 }{ m } } \)
  16. Solution

    4

  17. \( \displaystyle \frac{ \displaystyle \frac{ x + 1 }{ x } - \frac{ 5 }{ x + 2 } }{ \displaystyle \frac{ x + 1 }{ x^2 + 2x } + \frac{ 3 }{ x + 2 } } \)
  18. Solution

    \( \displaystyle \frac{x^2 - 2x + 2}{4x + 1}; x \ne 0, -2\)

  19. \( \displaystyle \frac{ \displaystyle \frac{ x + 1 }{x + 2 } + \frac{ x + 7 }{ x - 5} }{ \displaystyle \frac{5 }{ x^2 - 3x - 10 } } \)
  20. Solution

    \( \displaystyle \frac{2x^2 + 5x + 9}{5}; x \ne -2, 5\)

  21. \( \displaystyle \frac{ \displaystyle \frac{ a}{ b } + 2 + \frac{ b }{ a } }{ \displaystyle \frac{ a^2 - b^2 }{ ab } } \)
  22. Solution

    \( \displaystyle \frac{a + b}{a - b}\) for \( a, b \ne 0 \)

  23. \( \displaystyle \frac{ \displaystyle \frac{ 1 }{ cx^2 - 4c + dx^2 - 4d } + \frac{ 2 }{ cx + 2c + xd + 2d } }{ \displaystyle \frac{ 3 }{ x^2 - 4 } - \frac{ 4 }{ xc + xd - 2c - 2d } } \)
  24. Solution

    \( \displaystyle \frac{2x - 3}{3c + 3d - 4x - 8}\)