Упростите выражение[latex]( \frac{1}{x ^{2}-2xy+y ^{2} }- \frac{1}{x ^{2} -y ^{2} } ): \frac{2y ^{2} }{xy+x ^{2} } [/latex]

Question

Упростите выражение[latex]( \frac{1}{x ^{2}-2xy+y ^{2} }- \frac{1}{x ^{2} -y ^{2} } ): \frac{2y ^{2} }{xy+x ^{2} } [/latex]

Упростите выражение [latex]( \frac{1}{x ^{2}-2xy+y ^{2} }- \frac{1}{x ^{2} -y ^{2} } ): \frac{2y ^{2} }{xy+x ^{2} } [/latex]

Гость

Ответ(ы) на вопрос:

Accepted Answer

[latex](\frac{1}{x^2-2xy+y^2}-\frac{1}{x^2-y^2}):\frac{2y^2}{xy+x^2}=\\ (\frac{1}{(x-y)^2}-\frac{1}{(x-y)(x+y)}):\frac{2y^2}{x(x+y)}=\\ (\frac{x+y-x+y}{(x-y)(x+y)}):\frac{2y^2}{x(x+y)}=\\ \frac{2y}{(x-y)(x+y)}*\frac{x(x+y)}{2y^2}=\frac{x}{y(x-y)}[/latex]