Answer
$=\displaystyle \frac{1}{2},\qquad x\displaystyle \neq 5,-\frac{3}{2}$
Work Step by Step
Factor what you can:
$6x+9=3(2x+3)$
$3x-15=3(x-5)$
$x-5$ is factored
$4x+6=2(2x+3)$
Expression $=\displaystyle \frac{3(2x+3)}{3(x-5)}\cdot\frac{(x-5)}{2(2x+3)}\qquad$
...exclude the values that yield 0 in the denominator:
$x\displaystyle \neq 5,-\frac{3}{2}$
... cancel common factors: $3,\ (x-5)$, and $(2x+3)$
$=\displaystyle \frac{1}{2},\qquad x\displaystyle \neq 5,-\frac{3}{2}$
