Question

1. - / 1 points evaluate the limit, if it exists. (if an answer does not exist, enter dne.) $lim_{t

ightarrow0}left(\frac{3}{t}-\frac{3}{t^{2}+t}
ight)$ resources read it watch it

Explanation:

Step1: Find a common denominator

First, find a common - denominator for the two fractions. The common denominator of $t$ and $t^{2}+t=t(t + 1)$ is $t(t + 1)$. So, $\frac{3}{t}-\frac{3}{t^{2}+t}=\frac{3(t + 1)-3}{t(t + 1)}$.
\[

$$\begin{align*} \frac{3(t + 1)-3}{t(t + 1)}&=\frac{3t+3 - 3}{t(t + 1)}\\ &=\frac{3t}{t(t + 1)} \end{align*}$$

\]

Step2: Simplify the fraction

Cancel out the common factor $t$ in the numerator and the denominator. $\frac{3t}{t(t + 1)}=\frac{3}{t + 1}$ for $t
eq0$.

Step3: Evaluate the limit

Now, find $\lim_{t
ightarrow0}\frac{3}{t + 1}$. Substitute $t = 0$ into $\frac{3}{t + 1}$. We get $\frac{3}{0 + 1}=3$.

Answer:

$3$