Answer
$\dfrac{2x(2x+15)}{(x+7)(x+8)}$
Work Step by Step
We are given the rectangle with the dimensions:
$$\begin{align*}
\text{Length}&=\dfrac{x}{x+7}\\
\text{Width}&=\dfrac{x}{x+8}.
\end{align*}$$
We determine the perimeter of the rectangle:
$$\begin{align*}
\text{Perimeter}&=2\cdot\text{Length}+2\cdot\text{Width}\\
&=2\cdot\dfrac{x}{x+7}+2\cdot \dfrac{x}{x+8}\\
&=\dfrac{2x}{x+7}+\dfrac{2x}{x+8}\\
&=\dfrac{2x(x+8)+2x(x+7)}{(x+7)(x+8)}\\
&=\dfrac{2x(x+8+x+7)}{(x+7)(x+8)}\\
&=\dfrac{2x(2x+15)}{(x+7)(x+8)}.
\end{align*}$$
