Simplify the expression where $x>y>0$ Simplify $$\frac{\sqrt {x^2+y^2}+x}{y+\sqrt {x^2-y^2}}\cdot\frac{x-\sqrt {x^2+y^2}}{\sqrt {x^2-y^2}-y}$$
Help please, I tried but the answer doesn't match. I did it by multiplying of course and then normally simplifying.
I tried and what came is $\dfrac{-2xy -y^2}{2xy + x^2}$ and the correct answer is $\dfrac{y^2}{2y^2-x^2}$

$$\frac{\sqrt {x^2+y^2}+x}{y+\sqrt {x^2-y^2}}\cdot\frac{x-\sqrt {x^2+y^2}}{\sqrt {x^2-y^2}-y}= \frac{x + \sqrt {x^2+y^2}}{\sqrt {x^2-y^2}+y}\cdot\frac{x-\sqrt {x^2+y^2}}{\sqrt {x^2-y^2}-y}$$
Now you've got a function of the form $$\dfrac{(a+b)(a- b)}{(c+d)(c- d)} = \dfrac{a^2 - b^2}{c^2 - d^2}$$
The rest is then simplification.
