\begin{equation*}
\begin{split}
\frac{5a^2b(x+y)}{10a(x+y)^2}&=\frac{\cancel{5a(x+y)}(ab)}{\cancel{5a(x+y)}\cdot 2(x+y)}\:\:\:\:\:\color{blue} \text{take out the common factor } 5a(x+y)\\\\
\frac{5a^2b(x+y)}{10a(x+y)^2}& = \frac{ab}{2(x+y)}
\end{split}
\end{equation*}