Answer
$ -(x+3)^{1/2}(x+2)$
Work Step by Step
$\left[(x+3)^{3/2}=(x+3)^{1+\frac{1}{2}}=(x+3)(x+3)^{1/2}\right]$
$(x+3)^{1/2}-(x+3)^{3/2}=(x+3)^{1/2}-(x+3)(x+3)^{1/2}\qquad$
... factor out $(x+3)^{1/2}$
$=(x+3)^{1/2}[1-(x+3)]$
$=(x+3)^{1/2}(-x-2)\qquad$... factor out -1
$=-(x+3)^{1/2}(x+2)$
