Упростим каждую дробь:

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

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

[tex]\frac{1-x^{-1}y}{xy^{-1}+1} =\frac{1-\frac{y}{x}}{\frac{x}{y}+1}=\frac{\frac{x-y}{x} }{\frac{x+y}{y} }=\frac{y(x-y)}{x(x+y)}[/tex]

Тогда

[tex]\frac{x(x-y)^2}{(x+y)^2}\cdot \frac{1}{x}:\frac{y(x-y)}{x(x+y)}= \frac{(x-y)^2}{(x+y)^2}\cdot \frac{x(x+y)}{y(x-y)} =\frac{x(x-y)}{y(x+y)}[/tex]