Calculus Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 2

To write $\frac{1}{t}$ as a fraction with a common denominator, multiply by $\frac{t + 1}{t + 1}$ .

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

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{1}{t}$ by $\frac{t + 1}{t + 1}$ .

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Subtract $1$ from $1$ .

$\frac{t + 0}{t (t + 1)}$

Step 4.2

Add $t$ and $0$ .

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

Step 5

Cancel the common factor of $t$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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