Pre-Algebra Examples

$f (x) = \frac{x^{2} - 10 x + 24}{x^{2} + 4 x - 45}$

Step 1

Rewrite the function as an equation.

$y = \frac{x^{2} - 10 x + 24}{x^{2} + 4 x - 45}$

Step 2

Simplify $\frac{x^{2} - 10 x + 24}{x^{2} + 4 x - 45}$ .

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Step 2.1

Factor $x^{2} - 10 x + 24$ 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 $24$ and whose sum is $- 10$ .

$- 6, - 4$

Step 2.1.2

Write the factored form using these integers.

$y = \frac{(x - 6) (x - 4)}{x^{2} + 4 x - 45}$

Step 2.2

Factor $x^{2} + 4 x - 45$ 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 $- 45$ and whose sum is $4$ .

$- 5, 9$

Step 2.2.2

Write the factored form using these integers.

$y = \frac{(x - 6) (x - 4)}{(x - 5) (x + 9)}$