Limit of difference of two square roots I need to find the limit, not sure what to do.
$\lim_{x \to \infty} \sqrt{x^2 +ax} - \sqrt{x^2 +bx}$
I am pretty sure I have to divide by the largest degree which is x^2 but that gets me some weird numbers that don't seem to help.

Alternative Method:
One may write the limit as, $$\left(\lim_{x\to\infty}\sqrt{x^2+ax}-x\right)-\left(\lim_{x\to\infty}\sqrt{x^2‌​+bx}-x\right)\!\, \!,$$ and then use the standard techniques for evaluating limits of the form, $$\lim_{x\to\infty} \sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x,$$ to conclude that $\lim\limits_{x\to\infty}\sqrt{x^2+ax}-x=\tfrac a2$, and similarly $\lim\limits_{x\to\infty}\sqrt{x^2+bx}-x=\tfrac b2$, hence the limit is $\tfrac a2-\tfrac b2$.
