Question

In the following exercises, add.

$\frac{2w^2}{w^2-16}+\frac{8w}{w^2-16}$

Short answer

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

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{2w^2}{w^2-16}+\frac{8w}{w^2-16}$.

Step 2. Add the numerator

As the denominator is the same for both the terms, add the numerator and place it over the common denominator.

$\frac{2w^2+8w}{w^2-16}$

Step 3. Factor the expression  

• Factor the expression in the numerator and denominator, and then cancel out the common terms from the numerator and denominator.

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

• So, the resultant expression is $\frac{2w}{w-4}$.