Question

Add$\frac{8}{(t+5)}+\frac{6}{(t-5)}$.

Short answer

The sum is$\frac{14t-10}{(t+5)(t-5)}$.

Step-by-step solution

Given Information

The Given expression is$\frac{8}{(t+5)}+\frac{6}{(t-5)}$.

Find the LCD of denominators.

Since there are no common factors in denominators.

The LCD is$(t+5)(t-5)$.

Rewrite each fraction as an equivalent fraction with the LCD.

$=\frac{8(t-5)}{(t+5)(t-5)}+\frac{6(t+5)}{(t+5)(t-5)}$

Simplify numerator.

$=\frac{8t-40}{(t+5)(t-5)}+\frac{6t+30}{(t+5)(t-5)}$

Add

Take common denominator and simplify numerator.

$=\frac{8t-40+6t+30}{(t+5)(t-5)}$

$=\frac{14t-10}{(t+5)(t-5)}$