Algebra Examples

$\frac{x^{2} - 8 x - 9}{5 x^{2} - 45 x}$

Step 1

Factor $x^{2} - 8 x - 9$ 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 $- 9$ and whose sum is $- 8$ .

$- 9, 1$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 9) (x + 1)}{5 x^{2} - 45 x}$

Step 2

Simplify terms.

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Step 2.1

Factor $5 x$ out of $5 x^{2} - 45 x$ .

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Step 2.1.1

Factor $5 x$ out of $5 x^{2}$ .

$\frac{(x - 9) (x + 1)}{5 x (x) - 45 x}$

Step 2.1.2

Factor $5 x$ out of $- 45 x$ .

$\frac{(x - 9) (x + 1)}{5 x (x) + 5 x (- 9)}$

Step 2.1.3

Factor $5 x$ out of $5 x (x) + 5 x (- 9)$ .

$\frac{(x - 9) (x + 1)}{5 x (x - 9)}$

Step 2.2

Cancel the common factor of $x - 9$ .

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Step 2.2.1

Cancel the common factor.

$\frac{(x - 9) (x + 1)}{5 x (x - 9)}$

Step 2.2.2

Rewrite the expression.

$\frac{x + 1}{5 x}$