Answer
$a.\quad x\neq-4$
$ b.\quad$ Solution set = $\{-3\}$
Work Step by Step
$a.$
The denominators in the equation must not be zero:
$x+4\Rightarrow x\neq-4 \qquad(*)$
$b.$
Multiply both sides with the LCD,$\quad(x+4)$
$(x+4) \displaystyle \left[ \frac{3}{x+4}-7 \right] = (x+4) \left[ \dfrac{-4}{x+4} \right]\quad$ ... distribute and simplify
$ 3-7(x+4)=-4\quad$ ... distribute and simplify
$3-7x-28=-4$
$-7x-25=-4\quad$ ... add $25$ to both sides
$-7x=21$
$ x=-3 \quad$ ... satisfies (*), a valid solution.
Solution set = $\{-3\}$
