Question

Упростите выражение:

Answer 1

$1)\frac{x+2y}{x-2y}-\frac{x-2y}{x+2y}=\frac{x^{2}+4xy+4y^{2}-x^{2}+4xy-4y^{2}}{x^{2}-4y^{2}}=\frac{8xy}{x^{2}-4y^{2}}\\\\2)(\frac{8xy}{x^{2}-4y^{2}})^{-1}=\frac{x^{2}-4y^{2}}{8xy}\\\\3)\frac{x-2y}{(2xy)^{3} } :(xy)^{-2}=\frac{x-2y}{8x^{3}y^{3}}:\frac{1}{x^{2}y^{2}} =\frac{x-2y}{8x^{3}y^{3}}*x^{2}y^{2}=\frac{x-2y}{8xy}\\\\4)\frac{x^{2}-4y^{2}}{8xy}:\frac{x-2y}{8xy}=\frac{(x-2y)(x+2y)}{8xy}*\frac{8xy}{x-2y}=x+2y$