Answer
$a.\quad x\neq 1$
$ b.\quad$ Solution set = $\{3\}$
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,$\quad(x-1)$
$(x-1)\left[ \displaystyle \frac{1}{x-1}+5 \right] = (x-1)\left[ \dfrac{11}{x-1} \right]\quad$ ... distribute and simplify
$ 1+5(x-1)=11\quad$ ... distribute and simplify
$1+5x-5=11$
$ 5x-4=11\quad$ ... add $4$ to both sides
$5x=15$
$ x=3\quad$ ... satisfies (*), a valid solution.
Solution set = $\{3\}$
