Explanation

(a)
We have,
$y = \sqrt{\frac{(x + 1)(x - 3)}{(x - 2)}}$ here $x$ cannot be 2.
$\therefore Either\ both\ N^{r}\ and\ D^{r}$ are positive.
$x \geq - 1,\ x \geq 3\ \ and\ x > 2$
$\Rightarrow \ x \geq 3$ ….(i)
or $N^{r}$ is negative and $D^{r}$ is negative.
$x \geq - 1\ and\ x > 2$
$\Rightarrow - 1 \leq x < 2$ …(ii)
From Eqs. (i) and (ii), we get
$- 1 \leq x < 2\ \ or\ x \geq 3$