Basic Math Examples

$\frac{4 w^{2} - 8 w}{w^{2} - 7 w - 18} \div \frac{w - 2}{w + 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 w^{2} - 8 w}{w^{2} - 7 w - 18} \cdot \frac{w + 2}{w - 2}$

Step 2

Factor $4 w$ out of $4 w^{2} - 8 w$ .

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Step 2.1

Factor $4 w$ out of $4 w^{2}$ .

$\frac{4 w (w) - 8 w}{w^{2} - 7 w - 18} \cdot \frac{w + 2}{w - 2}$

Step 2.2

Factor $4 w$ out of $- 8 w$ .

$\frac{4 w (w) + 4 w (- 2)}{w^{2} - 7 w - 18} \cdot \frac{w + 2}{w - 2}$

Step 2.3

Factor $4 w$ out of $4 w (w) + 4 w (- 2)$ .

$\frac{4 w (w - 2)}{w^{2} - 7 w - 18} \cdot \frac{w + 2}{w - 2}$

Step 3

Factor $w^{2} - 7 w - 18$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 18$ and whose sum is $- 7$ .

$- 9, 2$

Step 3.2

Write the factored form using these integers.

$\frac{4 w (w - 2)}{(w - 9) (w + 2)} \cdot \frac{w + 2}{w - 2}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $w - 2$ .

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Step 4.1.1

Factor $w - 2$ out of $4 w (w - 2)$ .

$\frac{(w - 2) (4 w)}{(w - 9) (w + 2)} \cdot \frac{w + 2}{w - 2}$

Step 4.1.2

Cancel the common factor.

$\frac{(w - 2) (4 w)}{(w - 9) (w + 2)} \cdot \frac{w + 2}{w - 2}$

Step 4.1.3

Rewrite the expression.

$\frac{4 w}{(w - 9) (w + 2)} (w + 2)$

Step 4.2

Cancel the common factor of $w + 2$ .

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Step 4.2.1

Factor $w + 2$ out of $(w - 9) (w + 2)$ .

$\frac{4 w}{(w + 2) (w - 9)} (w + 2)$

Step 4.2.2

Cancel the common factor.

$\frac{4 w}{(w + 2) (w - 9)} (w + 2)$

Step 4.2.3

Rewrite the expression.

$\frac{4 w}{w - 9}$