Calculus Examples

$lim_{x \to 0} \frac{1}{t} - \frac{1}{t^{2} + t}$

Step 1

Evaluate the limit of $\frac{1}{t} - \frac{1}{t^{2} + t}$ which is constant as $x$ approaches $0$ .

$\frac{1}{t} - \frac{1}{t^{2} + t}$

Step 2

Factor $t$ out of $t^{2} + t$ .

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Step 2.1

Factor $t$ out of $t^{2}$ .

$\frac{1}{t} - \frac{1}{t \cdot t + t}$

Step 2.2

Raise $t$ to the power of $1$ .

$\frac{1}{t} - \frac{1}{t \cdot t + t^{1}}$

Step 2.3

Factor $t$ out of $t^{1}$ .

$\frac{1}{t} - \frac{1}{t \cdot t + t \cdot 1}$

Step 2.4

Factor $t$ out of $t \cdot t + t \cdot 1$ .

$\frac{1}{t} - \frac{1}{t (t + 1)}$