Algebra Examples

$\frac{1}{x - 10} \div \frac{9 x}{x^{2} - 9 x - 10}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{x - 10} \cdot \frac{x^{2} - 9 x - 10}{9 x}$

Step 2

Factor $x^{2} - 9 x - 10$ using the AC method.

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Step 2.1

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 $- 10$ and whose sum is $- 9$ .

$- 10, 1$

Step 2.2

Write the factored form using these integers.

$\frac{1}{x - 10} \cdot \frac{(x - 10) (x + 1)}{9 x}$

Step 3

Cancel the common factor of $x - 10$ .

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Step 3.1

Cancel the common factor.

$\frac{1}{x - 10} \cdot \frac{(x - 10) (x + 1)}{9 x}$

Step 3.2

Rewrite the expression.

$\frac{x + 1}{9 x}$