Calculus Examples

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

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

Step 1

Factor

t

$t$ out of

t^{2} + t

$t^{2} + t$ .

Tap for more steps...

Step 1.1

Factor

t

$t$ out of

t^{2}

$t^{2}$ .

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

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

Step 1.2

Raise

t

$t$ to the power of

1

$1$ .

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

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

Step 1.3

Factor

t

$t$ out of

t^{1}

$t^{1}$ .

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

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

Step 1.4

Factor

t

$t$ out of

t \cdot t + t \cdot 1

$t \cdot t + t \cdot 1$ .

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

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

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

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

Step 2

To write

\frac{1}{t}

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

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

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

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

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Multiply

\frac{1}{t}

$\frac{1}{t}$ by

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

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

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

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

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

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Subtract

1

$1$ from

1

$1$ .

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

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

Step 4.2

Add

t

$t$ and

0

$0$ .

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

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

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

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

Step 5

Cancel the common factor of

t

$t$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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