Rationalizing a numerator I'm having trouble rationalizing a numerator with radicals. After multiplying the conjugate I get 0. Does anyone know where I went wrong?
\begin{align}
\frac{\sqrt{2+y} + \sqrt{2 - y}}{y} & = \left(\frac{\sqrt{2+y} + \sqrt{2 - y}}{y}\right) \left(\frac{\sqrt{2+y} - \sqrt{2 - y}}{\sqrt{2+y} - \sqrt{2 - y}}\right)\\
& = \frac{\sqrt{2+y}\sqrt{2+y} - \sqrt{2+y}\sqrt{2-y} + \sqrt{2-y}\sqrt{2+y} - \sqrt{2-y}\sqrt{2-y}}{y\sqrt{2+y} - y\sqrt{2-y}}\\
& =\frac{2 + y - 2 - y}{y\sqrt{2+y} - y\sqrt{2-y}} = 0
\end{align}

Careful:
$$(a-b)(a+b)=a^2-b^2\implies $$
$$\left(\sqrt{2+y}+\sqrt{2-y}\right)\left(\sqrt{2+y}-\sqrt{2-y}\right)=(2+y)-(2-y)=2+y-2+y=2y$$
you forgot to change the second$\,-y\,$ into $\,+y\,$ ....
