Addition and Subtraction of Fractions.

7. ${\displaystyle \frac{7}{9-a^2}}-{\displaystyle \frac{1}{3+a}}-{\displaystyle \frac{1}{3-a}}$.

8. ${\displaystyle \frac{1}{a-b}}-{\displaystyle \frac{1}{a+b}}-{\displaystyle \frac{b}{a^2-b^2}}$.

9. ${\displaystyle \frac{2}{x-2}}-{\displaystyle \frac{2}{x+2}}+{\displaystyle \frac{5x}{x^2-4}}$.

10. ${\displaystyle \frac{3-x}{1-3x}}-{\displaystyle \frac{3+x}{1+3x}}-{\displaystyle \frac{15x-1}{1-9x^2}}$.

11. ${\displaystyle \frac{1}{a}}-{\displaystyle \frac{1}{a+3}}+{\displaystyle \frac{3}{a+1}}$.

12. ${\displaystyle \frac{x}{x-1}}-{\displaystyle \frac{1}{-}}{\displaystyle \frac{1}{x+1}}$.

13. ${\displaystyle \frac{x+1}{x+2}}+{\displaystyle \frac{x-2}{x-3}}+{\displaystyle \frac{2x+7}{x^2-x-6}}$.

14. ${\displaystyle \frac{1}{x(x-1)}}-{\displaystyle \frac{2}{x^2-1}}+{\displaystyle \frac{1}{x(x+1)}}$.

Exercise 48.

Find the sum of:

1. ${\displaystyle \frac{1}{2x+1}}+{\displaystyle \frac{1}{2x-1}}-{\displaystyle \frac{4x}{4x^2-1}}$.

2. ${\displaystyle \frac{a^2+b^2}{a^2-b^2}}+{\displaystyle \frac{a}{a+b}}-{\displaystyle \frac{b}{a-b}}$.

3. ${\displaystyle \frac{3a}{1-a^2}}+{\displaystyle \frac{2}{1-a}}-{\displaystyle \frac{2}{1+a}}$.

4. ${\displaystyle \frac{1}{2x+5y}}-{\displaystyle \frac{3x}{4x^2-25y^2}}+{\displaystyle \frac{1}{2x+5y}}$.

5. ${\displaystyle \frac{1}{x+4y}}-{\displaystyle \frac{8y}{x^2-16y^2}}+{\displaystyle \frac{1}{x-4y}}$.

6. ${\displaystyle \frac{3}{2x-3}}-{\displaystyle \frac{2}{2x+3}}-{\displaystyle \frac{3}{4x^2-9}}$.