Pre-Algebra Examples

$h (x) = \frac{x^{2} - 6 x - 16}{x^{2} + 6 x - 27}$

Step 1

Rewrite the function as an equation.

$y = \frac{x^{2} - 6 x - 16}{x^{2} + 6 x - 27}$

Step 2

Simplify $\frac{x^{2} - 6 x - 16}{x^{2} + 6 x - 27}$ .

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Step 2.1

Factor $x^{2} - 6 x - 16$ 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 $- 16$ and whose sum is $- 6$ .

$- 8, 2$

Step 2.1.2

Write the factored form using these integers.

$y = \frac{(x - 8) (x + 2)}{x^{2} + 6 x - 27}$

Step 2.2

Factor $x^{2} + 6 x - 27$ 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 $- 27$ and whose sum is $6$ .

$- 3, 9$

Step 2.2.2

Write the factored form using these integers.

$y = \frac{(x - 8) (x + 2)}{(x - 3) (x + 9)}$