Answer
1
Work Step by Step
$\lim\limits_{t \to 0}(\frac{1}{t}-\frac{1}{t^2+t})=\lim\limits_{t \to 0}(\frac{t^2+t}{t(t^2+t)}-\frac{t}{t(t^2+t)})=\lim\limits_{t \to 0}\frac{t^2+t-t}{t(t^2+t)}=\lim\limits_{t \to 0}\frac{t}{t^2+t}=\lim\limits_{t \to 0}\frac{1}{t+1}=\frac{1}{(0)+1}=1$
