Question

Subtract$\frac{y-4}{y+1}-\frac{1}{y+7}$.

Short answer

The difference is$\frac{y^2-2y-29}{(y+1)(y+7)}$.

Step-by-step solution

Given Information   

The Given expression is $\frac{y-4}{y+1}-\frac{1}{y+7}$.

Find the LCD of denominators. 

Since there are no common denominators.

The LCD is$(y+1)(y+7)$.

Rewrite each fraction as an equivalent fraction with the LCD.   

$=\frac{(y-4)(y+7)}{(y+1)(y+7)}-\frac{1(y+1)}{(y+1)(y+7)}$

Simplify the numerator.

$=\frac{y^2-4y+7y-28}{(y+1)(y+7)}-\frac{y+1}{(y+1)(y+7)}$

$=\frac{y^2-3y-28}{(y+1)(y+7)}-\frac{y+1}{(y+1)(y+7)}$

Subtract and simplify the numerator.  

Take common denominator.

$=\frac{y^2-3y-28-(y+1)}{(y+1)(y+7)}$

Simplify.

$=\frac{y^2-3y-28-y-1}{(y+1)(y+7)}$

$=\frac{y^2-2y-29}{(y+1)(y+7)}$.