Add and Subtract Rational Expressions with a Common Denominator: example 8.32

$\begin{array}{cccc}& & & \hfill \frac{7x+12}{x+3}+\frac{x^2}{x+3}\hfill \\ \\ \\ \begin{array}{c}\text{The fractions have a common}\hfill \\ \text{denominator, so add the numerators and}\hfill \\ \text{place the sum over the common}\hfill \\ \text{denominator.}\hfill \end{array}\hfill & & & \hfill \frac{7x+12+x^2}{x+3}\hfill \\ \\ \\ \text{Write the degrees in descending order.}\hfill & & & \hfill \frac{x^2+7x+12}{x+3}\hfill \\ \\ \\ \text{Factor the numerator.}\hfill & & & \hfill \frac{\left(x+3\right)\left(x+4\right)}{x+3}\hfill \\ \\ \\ \text{Simplify by removing common factors.}\hfill & & & \hfill \frac{\cancel{\left(x+3\right)}\left(x+4\right)}{\cancel{x+3}}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & \hfill x+4\hfill \end{array}$