Finding the limit of a function . How can I calculate the following limit:
\begin{equation*}
\lim_{x \rightarrow a}
\frac{\sqrt{x} - \sqrt{a} + \sqrt{x-a} }{\sqrt{x^2 - a^2}}
\end{equation*}
I feel that I should multiply by the conjugate, but which conjugate? 

Hint: Write $y=\sqrt{x}$ and $b=\sqrt{a}$. Then you get:$${y-b+\sqrt{y^2-b^2}\over \sqrt{y^4-b^4}}={\sqrt{y-b}+\sqrt{y+b}\over \sqrt{(y+b)(y^2+b^2)}}$$ So the limit is $1\over \sqrt{2a}$.
