Answer
$$\frac{10x-14}{\left(x+4\right)\left(x-5\right)}$$
Work Step by Step
The perimeter of a rectangle is equal to the sum of twice the length of each of the adjacent sides. Doing this, we find:
$$ \frac{6}{x+4}+\frac{4}{x-5}\\ \frac{6\left(x-5\right)}{\left(x+4\right)\left(x-5\right)}+\frac{4\left(x+4\right)}{\left(x-5\right)\left(x+4\right)}\\ \frac{6\left(x-5\right)+4\left(x+4\right)}{\left(x+4\right)\left(x-5\right)}\\ \frac{10x-14}{\left(x+4\right)\left(x-5\right)}$$
