Question

x/(x - y) + x/(x + y) + (x ^ 2 + y ^ 2)/(y ^ 2 - x ^ 2)

Answer 1

Ответ:

$\displaystyle 1$

Объяснение:

$\displaystyle \frac{x}{x - y} + \frac{x}{x + y} +\frac{x ^ 2 + y ^ 2}{y ^ 2 - x ^ 2}=\\\\\\ \frac{x}{x - y} + \frac{x}{x + y} -\frac{x ^ 2 + y ^ 2}{x ^ 2 - y ^ 2}=\\\\\\ \frac{x}{x - y} + \frac{x}{x + y} -\frac{x ^ 2 + y ^ 2}{(x-y)(x+y)}=\\\\\\ \frac{x(x+y)}{(x - y)(x+y)} + \frac{x(x-y)}{(x + y)(x-y)} -\frac{x ^ 2 + y ^ 2}{(x-y)(x+y)}=\\\\\\ \frac{x(x+y) +x(x-y) -(x ^ 2 + y ^ 2)}{(x-y)(x+y)}=\\\\\\ \frac{x^2+xy+x^2-xy-x^2-y^2}{(x-y)(x+y)}= \frac{x^2-y^2}{x^2-y^2}=1$