Algebra Examples

$\frac{x + 6}{x^{2} - 2 x - 48} \cdot (x^{2} - 4 x - 32)$

Step 1

Factor $x^{2} - 2 x - 48$ using the AC method.

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Step 1.1

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 $- 48$ and whose sum is $- 2$ .

$- 8, 6$

Step 1.2

Write the factored form using these integers.

$\frac{x + 6}{(x - 8) (x + 6)} \cdot (x^{2} - 4 x - 32)$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x + 6$ .

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Step 2.1.1

Cancel the common factor.

$\frac{x + 6}{(x - 8) (x + 6)} \cdot (x^{2} - 4 x - 32)$

Step 2.1.2

Rewrite the expression.

$\frac{1}{x - 8} \cdot (x^{2} - 4 x - 32)$

Step 2.2

Multiply $\frac{1}{x - 8}$ by $x^{2} - 4 x - 32$ .

$\frac{x^{2} - 4 x - 32}{x - 8}$

Step 3

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

$- 8, 4$

Step 3.2

Write the factored form using these integers.

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

Step 4

Cancel the common factor of $x - 8$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $x + 4$ by $1$ .

$x + 4$