Pre-Algebra Examples

$f (x) = \frac{x^{2} + 4 x - 32}{x^{2} + x - 56}$

Step 1

Rewrite the function as an equation.

$y = \frac{x^{2} + 4 x - 32}{x^{2} + x - 56}$

Step 2

Simplify $\frac{x^{2} + 4 x - 32}{x^{2} + x - 56}$ .

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Step 2.1

Factor $x^{2} + 4 x - 32$ using the AC method.

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Step 2.1.1

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 $- 32$ and whose sum is $4$ .

$- 4, 8$

Step 2.1.2

Write the factored form using these integers.

$y = \frac{(x - 4) (x + 8)}{x^{2} + x - 56}$

Step 2.2

Factor $x^{2} + x - 56$ using the AC method.

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Step 2.2.1

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 $- 56$ and whose sum is $1$ .

$- 7, 8$

Step 2.2.2

Write the factored form using these integers.

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

Step 2.3

Cancel the common factor of $x + 8$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$y = \frac{x - 4}{x - 7}$