Question

In the following exercises, add.

$\frac{7x^2}{x^2-9}+\frac{21x}{x^2-9}$

Short answer

The simplified expression is$\frac{7x}{x-3}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{7x^2}{x^2-9}+\frac{21x}{x^2-9}$.

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.

$\frac{7x^2}{x^2-9}+\frac{21x}{x^2-9}=\frac{7x^2+21x}{x^2-9}$

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.

$\frac{7x(x+3)}{(x-3)(x+3)}=\frac{7x}{x-3}$

• So, the resultant expression is $\frac{7x}{x-3}$.