Answer
(a) yes
(b) no
Work Step by Step
(a) Using $x=2$, we get:
Left side:
$\displaystyle \frac{1}{2}-\frac{1}{2-4}=\frac{1}{2}-\frac{1}{-2}=\frac{1}{2}+\frac{1}{2}=1$
Right side:
$1$
The sides match, so $x=2$ is a solution.
(b) Using $x=4$, we get:
Left side:
$\displaystyle \frac{1}{4}-\frac{1}{4-4}=undefined$
So $x=4$ is not a solution.
