Answer
Solution set = $\displaystyle \{\frac{9}{7}\}$.
Work Step by Step
First, we exclude those values of x that yield a zero in any of the denominators.
$x\not\in\{-1,-5\}\qquad (*)$
Multiply the equation with the LCD=$(x+5)(x+1)$
$(x-6)(x+1)=(x-3)(x+5)\qquad$ ... simplify (distribute)
$x^{2}+x-6x-6=x^{2}+5x-3x-15$
$ x^{2}-5x-6=x^{2}+2x-15\qquad$ ... add $6-x^{2}-2x$
$-5x-2x=-15+6$
$-7x=-9$
$ x=\displaystyle \frac{9}{7}\qquad$ ...Checking (*), this is a valid solution
Solution set = $\displaystyle \{\frac{9}{7}\}$.
