Answer
$a.\quad x\neq 2$
$ b.\quad$ Solution set = $\emptyset$
Work Step by Step
$a.$
The denominators in the equation must not be zero:
$x-2\Rightarrow x\neq 2 \qquad(*)$
$b.$
Multiply both sides with the LCD,$\quad(x-2)$
$(x-2) \displaystyle \left[ \frac{2}{x-2} \right] = (x-2) \left[ \frac{x}{x-2}-2 \right]\quad$ ... distribute and simplify
$ 2=x-2(x-2)\quad$ ... distribute and simplify
$2=x-2x+4$
$ 2=-x+4\quad$ ... add $x-2$ to both sides
$ x=2 \quad$ ... clashes with (*), not a valid solution.
Solution set = $\emptyset$
