First, you really need to put () around the numerator in the first line!

You factored the second line wrong.

y" = {(t+1)^3(-1) - [(1-t)(3)(t+1)^2]}/(t+1)^6

Taking a common (t+1)^2 from the first and second terms gives:

y'' = (t+1)^2{-(t+1) - 3(1-t)}/(t+1)^6

y'' = (t+1)^2{2t-4}/(t+1)^6

y'' = 2(t-2)/(t+1)^4

-Dan