# Honors Algebra 2: Extra Practice on Compound Fractions

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

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Simplify Fully.

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

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