Addition and Subtraction of Fractions.

4. ${\displaystyle \frac{3x-2}{9}}-{\displaystyle \frac{x-2}{6}}+{\displaystyle \frac{5x+3}{4}}$.

5. ${\displaystyle \frac{x-1}{6}}-{\displaystyle \frac{x-3}{3}}+{\displaystyle \frac{x-5}{2}}$.

6. ${\displaystyle \frac{x-2y}{2x}}+{\displaystyle \frac{x+5y}{4x}}-{\displaystyle \frac{x+7y}{8x}}$.

7. ${\displaystyle \frac{5x-11}{3}}-{\displaystyle \frac{2x-1}{10}}-{\displaystyle \frac{11x-5}{15}}$.

8. ${\displaystyle \frac{x-3}{3x}}-{\displaystyle \frac{x^2-6x}{5x^2}}-{\displaystyle \frac{7x^2-x^3}{15x^3}}$.

9. ${\displaystyle \frac{ac-b^2}{ac}}-{\displaystyle \frac{ab-c^2}{ab}}+{\displaystyle \frac{a^2-bc}{bc}}$.

134. When the denominators have compound expressions, arranged in the same order.

1. Simplify ${\displaystyle \frac{a+b}{a-b}}-{\displaystyle \frac{a-b}{a+b}}-{\displaystyle \frac{4ab}{a^2-b^2}}$.

The L. C. D. is $(a-b)(a+b)$.

The multipliers are $a+b$, $a-b$, and $1$, respectively.

{l*{3}{cr}cl} (a + b)(a + b) &=& a^{2} &+& 2ab &+& b^{2} &=& \text{1st numerator.} \ \llap{$-$} (a - b)(a - b) &=&-a^{2} &+& 2ab &-& b^{2} &=& \text{2d numerator.} \ \llap{$-$} 1(4ab) &=& &-& 4ab & & &=& \text{3d numerator.} \ \cline{3-7} & & \multicolumn{5}{c}{0} &=& \text{sum of numerators.} \ \therefore\ \text{Sum of fractions$=0$.}

Exercise 47.

Find the sum of:

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

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

3. ${\displaystyle \frac{4}{x-8}}-{\displaystyle \frac{1}{x+2}}$.

4. ${\displaystyle \frac{a+x}{a-x}}-{\displaystyle \frac{a-x}{a+x}}$.

5. ${\displaystyle \frac{x}{x-a}}-{\displaystyle \frac{x^2}{x^2-a^2}}$.

6. ${\displaystyle \frac{4a^2+b^2}{4a^2-b^2}}-{\displaystyle \frac{2a+b}{2a-b}}$.