Question

Subtract$\frac{w+2}{w+4}-\frac{w}{w-2}$.

Short answer

The difference is$\frac{-4(w+1)}{(w+4)(w-2)}$.

Step-by-step solution

Given Information  

The Given expression is$\frac{w+2}{w+4}-\frac{w}{w-2}$.

Find the LCD of denominators.  

Since there are no common denominators.

The LCD is$(w+4)(w-2)$.

Rewrite each fraction as an equivalent fraction with the LCD.  

$=\frac{(w+2)(w-2)}{(w+4)(w-2)}-\frac{w(w+4)}{(w+4)(w-2)}$

Simplify.

$=\frac{w^2-2w+2w+4}{(w+4)(w-2)}-\frac{w^2+4w}{(w+4)(w-2)}$

Subtract and simplify the numerator. 

Take common denominator.

$=\frac{w^2+4-(w^2+4w)}{(w+4)(w-2)}$

$=\frac{w^2+4-w^2-4w}{(w+4)(w-2)}$

$=\frac{4-4w}{(w+4)(w-2)}$

$=\frac{-4(w+1)}{(w+4)(w-2)}$