Pre-Algebra Examples

$g (x) = \frac{x^{2} + 2 x - 8}{x^{2} - 4 x - 12}$

Step 1

Write $g (x) = \frac{x^{2} + 2 x - 8}{x^{2} - 4 x - 12}$ as an equation.

$y = \frac{x^{2} + 2 x - 8}{x^{2} - 4 x - 12}$

Step 2

Simplify $\frac{x^{2} + 2 x - 8}{x^{2} - 4 x - 12}$ .

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Step 2.1

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

$- 2, 4$

Step 2.1.2

Write the factored form using these integers.

$y = \frac{(x - 2) (x + 4)}{x^{2} - 4 x - 12}$

Step 2.2

Factor $x^{2} - 4 x - 12$ 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 $- 12$ and whose sum is $- 4$ .

$- 6, 2$

Step 2.2.2

Write the factored form using these integers.

$y = \frac{(x - 2) (x + 4)}{(x - 6) (x + 2)}$

Step 3

The given equation $y = \frac{(x - 2) (x + 4)}{(x - 6) (x + 2)}$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$