Answer
$=\displaystyle \frac{x}{x-2}, \quad x\neq 2$
Work Step by Step
The fractions have a common denominator, we subtract the numerators...
$\displaystyle \frac{2x+3}{3x-6}-\frac{3-x}{3x-6}=\frac{2x+3-(3-x)}{3x-6}$
$=\displaystyle \frac{3x}{3x-6}$
... factor what we can...
$=\displaystyle \frac{3x}{3(x-2)}$
... exclude values that yield 0 in the denominator:
$x\neq 2$
... and, cancel the common factor
$=\displaystyle \frac{x}{x-2}, \quad x\neq 2$
