Calculate $\lim_{x \rightarrow a} \frac{x^2 + ax - 2a^2}{\sqrt{2x^2 - ax} -a}$ I need to calculate:
$$\lim_{x \rightarrow a} \frac{x^2 + ax - 2a^2}{\sqrt{2x^2 - ax} -a}$$
I get $0/0$ and can then use l'hopital's rule to find the limit, I can do this but someone asked me how I can do this without using l'hopital's rule. I guess I have to seperate $(x-a)$ in the nominator and denominator. The nominator can be written as $(x-a)(x+a)$ but I don't see how to seperate $(x-a)$.

Hint. Note that for $x\not=a$,
$$\frac{x^2 + ax - 2a^2}{\sqrt{2x^2 - ax} -a}=\frac{(x+2a)(x-a)(\sqrt{2x^2 - ax} +a)}{(2x+a)(x-a)}.$$
