please help fix this math problem!!!?

Question

http://answers.yahoo.com/question/index?qid=20070903112434AAAKao8&r=w
this is my another problem
somebody tell me how to do it
but i don know how to fix:(t^3+3t^2-12t+4)/(t-2)

Answer 1

(t^3+3t^2-12t+4)/(t-2) = t^2+5t-2 for all t not =2
Use synthetic division to factorize the numerator
t^3-4t = t(t+2)(t-2)
so simplifying
= (t^2+5t-2)/t(t+2) = 12/8 = 3/2