(t^2 + 2t + 4) / (t+1)

topscore talks about subtracting (t^2 + t) from the first parentheses, and then subtracting the (t+1) from the remainder (t+4) to get the answer of

(t+1) + 3/(t+1)

sure i can smile and nod the whole time, but i don't understand the "why" of any of it, and i don't ever really remember learning this... can someone please try and explain a little? muchos gracias!