Cannot for the life of me follow this simplification

http://i.imgur.com/6HvVncv.jpg

I understand how the sqrt comes down, from the right half of the top, but how does the top left part lose the square root?

After simplifying, I can get

sqrt(x^2+1) - x^2 / (x^2+1)^(3/2)

However, the answer that all online calcs give and my tutorial notes give is

1/ (x^2+1)^(3/2)

And I can see where that is going from the working up the top, but can't figure out how the sqrt(x^2+1) turns into (x^2+1)

Re: Cannot for the life of me follow this simplification

One way to see this is to factor, first cancel the 2 with 1/2 at top right then factor

Notice if you distribute, the bases are the same so you add exponents and keep the base , -1/2 + 1 = 1/2 so we're good

Next simplify within brackets = 1 then bring what's left to the denominator so it's exponent is positive, finally keep the same base and add the exponents. Let me know if you need more details.

:)

Re: Cannot for the life of me follow this simplification

Yep,I definitely need more details with that first factoring. I have been sitting, trying to work this out for over two hours

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Re: Cannot for the life of me follow this simplification

Re: Cannot for the life of me follow this simplification