Pre-Algebra Examples

$\frac{w^{2} + 7 w + 12}{w + 3} \div \frac{w^{2} + 7 w + 12}{w^{2} - 1 w}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{w^{2} + 7 w + 12}{w + 3} \cdot \frac{w^{2} - 1 w}{w^{2} + 7 w + 12}$

Step 2

Cancel the common factor of $w^{2} + 7 w + 12$ .

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Step 2.1

Cancel the common factor.

$\frac{w^{2} + 7 w + 12}{w + 3} \cdot \frac{w^{2} - 1 w}{w^{2} + 7 w + 12}$

Step 2.2

Rewrite the expression.

$\frac{1}{w + 3} (w^{2} - 1 w)$

Step 3

Rewrite $- 1 w$ as $- w$ .

$\frac{1}{w + 3} (w^{2} - w)$

Step 4

Multiply $\frac{1}{w + 3}$ by $w^{2} - w$ .

$\frac{w^{2} - w}{w + 3}$

Step 5

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

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Step 5.1

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

$\frac{w \cdot w - w}{w + 3}$

Step 5.2

Factor $w$ out of $- w$ .

$\frac{w \cdot w + w \cdot - 1}{w + 3}$

Step 5.3

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

$\frac{w (w - 1)}{w + 3}$