Answer
Solution set = $\{1\}$.
Work Step by Step
First, we exclude those values of x that yield a zero in any of the denominators.
$x\not\in\{-5 \}\qquad (*)$
The first denominator $5x+5$ is factored as $5(x+1)$
Multiply the equation with the LCD=$3(x-4)$
$ 1=3(5)-7(x+1)\qquad$ ... simplify (distribute)
$1=15-7x-7$
$ 1=-7x+8\qquad$ ... add $-8$
$-7=-7x$
$ x=1 \qquad$ ...Checking (*), this is a valid solution
Solution set = $\{1\}$.
