Answer
$\frac{2x^2+3x-11}{(x-7)(x+2)}$
Work Step by Step
Given \begin{equation}
\frac{x+5}{x-7}+\frac{x+3}{x+2}.
\end{equation} The student added the numerators of the fractions without first expressing the fractions over a common denominator.
Find the LCD of the fractions which is: $\mathbf{LCD}=(x-7)(x+2)$. Perform addition:
\begin{equation}
\begin{aligned}
\frac{x+5}{x-7}+\frac{x+3}{x+2}&=\frac{(x+5)(x+2)}{(x-7)(x+2)}+\frac{(x+3)(x-7)}{(x-7)(x+2)} \\
&= \frac{x^2+7x+10+x^2-4x-21}{(x-7)(x+2)}\\
&= \frac{2x^2+3x-11}{(x-7)(x+2)}.
\end{aligned}
\end{equation}
