Answer
$ \frac{x^2+2x+15}{(x+3)(x-3)}$.
Work Step by Step
In order to add the two rational fractions, we must find the Least Common Denominator (LCD) of the kids.
The LCD is $(x+3)(x-3)$.
Multiply the numerator and the denominator to form LCD at the denominators.
$\Rightarrow \frac{x}{x+3}+ \frac{5}{x-3}=\frac{x(x-3)}{(x+3)(x-3)}+ \frac{5(x+3)}{(x+3)(x-3)}$
Use distributive property.
$\Rightarrow \frac{x^2-3x}{(x+3)(x-3)}+ \frac{5x+15}{(x+3)(x-3)}$
Add the numerators because denominators are same.
$\Rightarrow \frac{x^2-3x+5x+15}{(x+3)(x-3)}$
Add like terms.
$\Rightarrow \frac{x^2+2x+15}{(x+3)(x-3)}$.
