Question about reducing an answer from a derivative?

[Ascendant78]

Ok, I can get to the answer in yellow, but I am not sure how they went from the answer in yellow to the simplified one in white. I really need to know how to do this because we are using these derivatives for magnitudes (solving for principal normal unit vectors), where I have to square them and take square roots. So, I'm sure you could imagine having to square equations like this, factor out, try to take roots, etc., is a complete and utter nightmare. Each problem is taking me about 30-40mins, and there are 9 homework problems.

Anyway, here is the derivative:

 

[Simon Bridge]

Put your two terms over a common denominator, expand the brackets and extract 4t^3 as a common factor in the numerator.

 

[Ascendant78]

Put your two terms over a common denominator, expand the brackets and extract 4t^3 as a common factor in the numerator.

Ah, ok I see it now. Thanks again!

 

[Simon Bridge]

No worries. Well done.