sorry may have been at this too long but ive been blanking on this one for a while now, been coming at it different ways and I cannot work it down!

f(x) = x^2/sqrt(x^2-1)

so what i did for f'(x)

f(x) = x^2 * 1/sqrt(x^2-1)

product and chain rule to:

f'(x) = 2x/sqrt(x^2-1) - x^3/(x^2-1)^(3/2)

I cannot seem for the life of me to algebra this little rascal down a single term and I feel like I should be able to as solving in this state for the critical points is proving....lets use challenging.

Would really appreciate a point in the right direction!