Question

Subtract$\frac{t}{t-5}-\frac{t-1}{t+5}$.

Short answer

The result is$\frac{11t-5}{(t-5)(t+5)}$.

Step-by-step solution

Given Information   

The Given expression is$\frac{t}{t-5}-\frac{t-1}{t+5}$.

Find the LCD of denominators.    

Since there are no common denominators.

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

Rewrite each fraction as an equivalent fraction with the LCD.   

$=\frac{t(t+5)}{(t-5)(t+5)}-\frac{(t-1)(t-5)}{(t-5)(t+5)}$

$=\frac{t^2+5t}{(t-5)(t+5)}-\frac{t^2-t-5t+5}{(t-5)(t+5)}$

$=\frac{t^2+5t}{(t-5)(t+5)}-\frac{t^2-6t+5}{(t-5)(t+5)}$

Subtract and simplify the numerator.   

Take common denominator.

$=\frac{t^2+5t-(t^2-6t+5)}{(t-5)(t+5)}$

$=\frac{t^2+5t-t^2+6t-5}{(t-5)(t+5)}$

Simplify.

$=\frac{11t-5}{(t-5)(t+5)}$