Simplify. (Assume that the denominator is not 0.)
4(t − 1) + 4/4t + 4
the way you typed it ...
4(t − 1) + 4/4t + 4
= 4t - 4 + 1/t + 4
= 4t + 1/t
Something tells me you meant:
4/(t-1) + 4/(4t+4)
= 4/(t-1) + 1/(t+1) , the LCD is (t-1)(t+1)
= ( 4(t+1) + t-1)/((t-1)(t+1))
= (4t + 4 + t - 1)/(t^2 - 1)
= (5t + 3)/(t^2 - 1) , t ≠ ± 1