How to solve this limit? (difference of two square rooted terms)

[mnb96]

Hello,
do you have a hint on how to solve this limit?

$$\lim_{x\to +\infty}(\sqrt{x^2+ax+b}-\sqrt{x^2-ax+b})$$

Thanks!

 

[Petek]

When I see an expression of the form

$$\sqrt{A} - \sqrt{B}$$

I think of multiplying it by

$$\frac{\sqrt{A} + \sqrt{B}}{\sqrt{A} + \sqrt{B}}$$

Does that help?

Petek

 

[mnb96]

Thanks a lot!
that trick made the job. The limit of that expression is a