Answer
$\frac{-8 y-34}{(y+2)(y+4)}$
Work Step by Step
Given \begin{equation}
\frac{y-7}{y+2}-\frac{y+3}{y+4}.
\end{equation} First find the LCM of the fractions which is: $\mathbf{L C M}=(y+2)(y+4)$. Perform subtraction:\begin{equation}
\begin{aligned}
\frac{y-7}{y+2}-\frac{y+3}{y+4}&=\frac{(y-7)(y+4)}{(y+2)(y+4)}-\frac{(y+3)(y+2)}{(y+4)(y+2)} \\
&= \frac{(y-7)(y+4)-(y+3)(y+2)}{(y+2)(y+4)}\\
&= \frac{y^2-3 y-28 -y^2-5 y-6}{(y+2)(y+4)}\\
&=\frac{-8 y-34}{(y+2)(y+4)}.
\end{aligned}
\end{equation}
