Answer
$[2, \infty)$
Work Step by Step
$y=\displaystyle \frac{\sqrt{x-2}}{2x+3}$
For y to be defined,
1. the radicand in the numerator must not be negative, and
2. the denominator must not be zero
$\left[\begin{array}{lll}
1. & & 2.\\
x-2\geq 0 & & 2x+3\neq 0\\
x\geq 2 & & 2x\neq-3\\
& & x\neq-\frac{3}{2}
\end{array}\right]$
Domain: $[2, \infty)$
