下列等式中成立的是 $($ 　　 $)$

A．	${(-3x^{2}y)}^3=-9x^6{y}^3$	B．	$x^2={\left(\frac{x+1}{2}\right)}^2-{\left(\frac{x-1}{2}\right)}^2$
C．	$\sqrt{2}÷(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}})=2+\sqrt{6}$	D．	$\frac{1}{(x+1)(x+2)}=\frac{1}{x+1}-\frac{1}{x+2}$