Algebra Examples

$\frac{x + 2}{x^{2} - 6 x - 16} \div \frac{1}{9 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 2}{x^{2} - 6 x - 16} (9 x)$

Step 2

Rewrite using the commutative property of multiplication.

$9 \frac{x + 2}{x^{2} - 6 x - 16} x$

Step 3

Factor $x^{2} - 6 x - 16$ 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 $- 16$ and whose sum is $- 6$ .

$- 8, 2$

Step 3.2

Write the factored form using these integers.

$9 \frac{x + 2}{(x - 8) (x + 2)} x$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x + 2$ .

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Step 4.1.1

Cancel the common factor.

$9 \frac{x + 2}{(x - 8) (x + 2)} x$

Step 4.1.2

Rewrite the expression.

$9 \frac{1}{x - 8} x$

Step 4.2

Combine $9$ and $\frac{1}{x - 8}$ .

$\frac{9}{x - 8} x$

Step 4.3

Combine $\frac{9}{x - 8}$ and $x$ .

$\frac{9 x}{x - 8}$