Horride Limits. :(

[etotheipi]

Hi all.

Im really stuck on this problem. I need to resolve the limits on this:

\(\displaystyle \lim_{x \to \infty}x^{3/2}[(1+x+\frac{1}{x})^{1/2}-(1+x)^{1/2}]\)

Any help will be greatly appreciated.

 

[pka]

\(\displaystyle \left( {\sqrt {1 + x + \frac{1}{x}} - \sqrt {1 + x} } \right)\frac{{\left( {\sqrt {1 + x + \frac{1}{x}} + \sqrt {1 + x} } \right)}}{{\left( {\sqrt {1 + x + \frac{1}{x}} + \sqrt {1 + x} } \right)}} = \frac{{\frac{1}{x}}}{{\left( {\sqrt {1 + x + \frac{1}{x}} + \sqrt {1 + x} } \right)}}\)