Answer
Solution set = $\emptyset$.
(no solution)
Work Step by Step
The RHS denominator $x^{2}-9$ is a difference of squares.
$x^{2}-9=(x-3)(x+3)$
First, we exclude those values of x that yield a zero in any of the denominators.
$x\not\in\{-3,3 \}\qquad (*)$
Multiply the equation with the LCD=$(x-3)(x+3)$
$ 4x(x-3)-12(x+3)=4x^{2}+36\qquad$ ... simplify (distribute)
$4x^{2}-12x-12x-36=4x^{2}+36$
$ 4x^{2}-24x-36=4x^{2}+36\qquad$ ... add $36-4x^{2}$ to both sides
$-24x=36+36$
$x=-\displaystyle \frac{72}{24} $
$ x=-3\qquad$ ...Checking (*), this is not a valid solution
Solution set = $\emptyset$.
(no solution)
