Suma y resta de fracciones

(a - b)(a - b) &=&-a^{2} &+& 2ab &-& b^{2} &=& \text{2do numerador.} \ \llap{ − } 1(4ab) &=& &-& 4ab & & &=& \text{3er numerador.} \ \cline{3-7} & & \multicolumn{5}{c}{0} &=& \text{suma de numeradores.} \ \therefore\ \text{Suma de fracciones = 0 .}

Ejercicio 47.

Encuentra la suma de:

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

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