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## Homework Statement

Simplify the following:

[tex]\frac{\frac{1}{\sqrt{t^2+1}}-t^2(t^2+1)^{-3/2}}{\sqrt{\frac{1}{t^2+1}-\frac{2t^2}{(t^2+1)^2}+\frac{t^4+t^2}{(t^2+1)^3}}}[/tex]

## Homework Equations

The answer in the book was:

[tex]\frac{1}{\sqrt{t^2+1}}[/tex]

I didn't believe but then I graphed both functions and sure enough they are equivalent.

## The Attempt at a Solution

All I really knew to try was to factor out a 1/(t^2+1) inside the square root, but that really didn't help me see a different approach.

I'm hoping someone will have a neat trick for simplifying this mofo