Question

Упростить. ответ должен получится (x+y)/(x-y)​

Answer 1

Пошаговое объяснение:

$\frac{x^{4}-y^{4}}{x^{2}y^{2}} :[(1+\frac{y^{2}}{x^{2}})(1-\frac{2x}{y}+\frac{y^{2}}{x^{2}})]=\frac{(x^{2} -y^{2})(x^{2} +y^{2})}{x^{2}y^{2}} :[(\frac{x^{2}+y^{2}}{x^{2}})(\frac{x^2-2xy+y^{2}}{y^{2}})]=$

$\frac{(x-y)(x+y)(x^{2} +y^{2})}{x^{2}y^{2}} :[(\frac{x^{2}+y^{2}}{x^{2}})(\frac{(x-y)^{2}}{y^{2}})]=\frac{(x-y)(x+y)(x^{2} +y^{2})}{x^{2}y^{2}} *\frac{x^{2}y^{2}}{(x-y)^{2}*(x^{2} +y^{2})}=$

$=\frac{x+y}{x-y}$