Answer
$a.\quad x\neq-1$
$ b.\quad$ Solution set = $\emptyset$
Work Step by Step
$a.$
The denominators in the equation must not be zero:
$x+1\Rightarrow x\neq-1 \qquad(*)$
$b.$
Multiply both sides with the LCD,$\quad(x+1)$
$(x+1) \displaystyle \left[ \frac{8x}{x+1} \right] = (x+1) \left[ 4-\frac{8}{x+1} \right]\quad$ ... distribute and simplify
$ 8x=4(x+1)-8\quad$ ... distribute and simplify
$8x=4x+4-8$
$ 8x=4x-4\quad$ ... add $-4x$ to both sides
$4x=-4$
$ x=-1 \quad$ ... clashes with (*), not a valid solution.
Solution set = $\emptyset$
