Pre-Algebra Examples

$\frac{d^{2} - 1}{d^{2} - d} \div \frac{d + 1}{d - 1}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{d^{2} - 1}{d^{2} - d} \cdot \frac{d - 1}{d + 1}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{d^{2} - 1^{2}}{d^{2} - d} \cdot \frac{d - 1}{d + 1}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = d$ and $b = 1$ .

$\frac{(d + 1) (d - 1)}{d^{2} - d} \cdot \frac{d - 1}{d + 1}$

Step 3

Factor $d$ out of $d^{2} - d$ .

Tap for more steps...

Step 3.1

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

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

Step 3.2

Factor $d$ out of $- d$ .

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

Step 3.3

Factor $d$ out of $d \cdot d + d \cdot - 1$ .

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

Step 4

Cancel the common factor of $d + 1$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{d - 1}{d (d - 1)} (d - 1)$

Step 5

Cancel the common factor of $d - 1$ .

Tap for more steps...

Step 5.1

Factor $d - 1$ out of $d (d - 1)$ .

$\frac{d - 1}{(d - 1) d} (d - 1)$

Step 5.2

Cancel the common factor.

$\frac{d - 1}{(d - 1) d} (d - 1)$

Step 5.3

Rewrite the expression.

$\frac{d - 1}{d}$

Step 6

Split the fraction $\frac{d - 1}{d}$ into two fractions.

$\frac{d}{d} + \frac{- 1}{d}$

Step 7

Cancel the common factor of $d$ .

Tap for more steps...

Step 7.1

Cancel the common factor.

$\frac{d}{d} + \frac{- 1}{d}$

Step 7.2

Rewrite the expression.

$1 + \frac{- 1}{d}$

Step 8

Move the negative in front of the fraction.

$1 - \frac{1}{d}$