Algebra Examples

$\frac{x^{2} + 4 x - 32}{x^{2} + 9 x + 8} \div \frac{x + 7}{x + 1}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + 4 x - 32}{x^{2} + 9 x + 8} \cdot \frac{x + 1}{x + 7}$

Step 2

Factor $x^{2} + 4 x - 32$ 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 $- 32$ and whose sum is $4$ .

$- 4, 8$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 4) (x + 8)}{x^{2} + 9 x + 8} \cdot \frac{x + 1}{x + 7}$

Step 3

Factor $x^{2} + 9 x + 8$ 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 $8$ and whose sum is $9$ .

$1, 8$

Step 3.2

Write the factored form using these integers.

$\frac{(x - 4) (x + 8)}{(x + 1) (x + 8)} \cdot \frac{x + 1}{x + 7}$

Step 4

Cancel the common factor of $x + 1$ .

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Step 4.1

Cancel the common factor.

$\frac{(x - 4) (x + 8)}{(x + 1) (x + 8)} \cdot \frac{x + 1}{x + 7}$

Step 4.2

Rewrite the expression.

$\frac{(x - 4) (x + 8)}{x + 8} \cdot \frac{1}{x + 7}$

Step 5

Multiply $\frac{(x - 4) (x + 8)}{x + 8}$ by $\frac{1}{x + 7}$ .

$\frac{(x - 4) (x + 8)}{(x + 8) (x + 7)}$

Step 6

Cancel the common factor of $x + 8$ .

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Step 6.1

Cancel the common factor.

$\frac{(x - 4) (x + 8)}{(x + 8) (x + 7)}$

Step 6.2

Rewrite the expression.

$\frac{x - 4}{x + 7}$