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 $\dfrac{y^2}{2y^2-x^2}$

$(a+b)(a-b)=a^2-b^2$
So,
$[(\sqrt {x^2+y^2})+x]\cdot [x-(\sqrt {x^2+y^2})]=[x+(\sqrt {x^2+y^2})]\cdot [x-(\sqrt {x^2+y^2})]=x^2-(x^2+y^2)=-y^2$
Can you proceed?
