How to differentiate for critical points with variable in denominator

Question

sorry for posting a particular problem, this is maybe more of an algebra problem than a calculus problem, but it does involve differentiating so I thought I would state the problem as one. I am currently running through the openOnlineMIT multivariable calculus course. I have ran into a problem which I can't seem to come to the solution. Specifically I am trying to find $\frac{\mathrm{d}}{\mathrm{d}t} {4\over1+t^2+(1.5-t^2)^2} = 0 $ When I set this to zero I get ${1\over t(1-t^2)} = 0$. What I can't seem to understand how to solve the algebra. The answers given is $4t(t^2−1)=0$. which is a bit different but is solvable.

Answer 1

We have

$$\frac{d}{dt}\left( {4\over1+t^2+(1.5-t^2)^2}\right) = -\frac{16t^3-16t}{(t^4-2t^2+3.25)^2}$$

This is zero only when

$$16t^3-16t=0$$ $$16t(t^2-1)=0$$

Which is basically the answer you were given.

Did you make a mistake in taking the derivative?