Finding the limit as x approaches infinity with nested radicals

[coreluccio]

Homework Statement

Homework Equations

The Attempt at a Solution

This is a problem I have for a homework assignment. I punched it in on Wolfram, and there is the answer it gives. I can't figure out how to solve this thing. I tried multiplying by the conjugate radicals and simplifying, tried factoring out the highest power of x, but nothing seems to work.

 

[SammyS]

I see that WolframAlpha wouldn't show it's steps.

(sqrt(x^3-x^2)-sqrt(x^3+x^2*cos^(-1)((x^2+2x)/(2x^2+3x+1))))/(sqrt(x+3)-sqrt(2x+5))

http://www.wolframalpha.com/input/?...))))/(sqrt(x+3)-sqrt(2x+5))]+as+x->+infinity"