Answer
$\frac{3x^{2}+7x-45}{(3x-2)(3x+2)(x-5)}$
Work Step by Step
We simplify as follows:
$\frac{x}{3x^{2}-13x-10}+\frac{9}{9x^{2}-4}$
$=\frac{x}{(3x+2)(x-5)}+\frac{9}{(3x-2)(3x+2)}$
$=\frac{x(3x-2)}{(3x-2)(3x+2)(x-5)}+\frac{9(x-5)}{(3x-2)(3x+2)(x-5)}$
$=\frac{x(3x-2)+9(x-5)}{(3x-2)(3x+2)(x-5)}$
$=\frac{3x^{2}+7x-45}{(3x-2)(3x+2)(x-5)}$