Question

Упростите выражение:

Answer 1

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