<s>[INST] How to compute $\frac{t^2}{t+1}$ to the form $\frac{1}{t+1} +t -1$ One of my attempts would look like below.
$\frac{t^2}{t+1}$ = $\frac{t \times t+1-1}{t+1}$ = 1+ $\frac{t-1}{t+1}$ = $\frac{t-1+1-1}{t+1} + 1$ = $\frac{-2}{t+1} +2$
Also, I put into t an arbitrary number in both equations and have gotten the same answer. The first number was 18785 to which both contained the answer $\frac{352876225}{18786}$. 
 [/INST] we have $$\frac{t^2}{t+1}=\frac{t^2-1+1}{t+1}=\frac{(t-1)(t+1)+1}{t+1}$$
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