Simplifying sqrt(4t^2+4+1/t^2) to (1+2t^2)/t

[snoggerT]

reducing sqrt(4t^2+4+1/t^2) to (1+2t^2)/t

The Attempt at a Solution

- This is actually just a portion of a calculus problem, but I can't figure out how the book did the algebra here. I get (2t^2+2t+1)/t and don't know how that reduces to (1+2t^2)/t. Please help.

 

[Dick]

Factor the 1/t^2 out as 1/t. Then 4*t^4+4*t^2+1=(2*t^2+1)^2.

 

[Petkovsky]

Put the whole thing under a single fraction : (4t^4 + 4t^2 + 1) / t^2
Now above you have a complete square so you can simplify this and when you do the square root you get the exact solution