Question

Упростите выражение (x+y/x-y  -  x-y/x+y) : xy/x^2-y^2

Answer 1

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