Algebra Examples

$\frac{{(x - 7)}^{2}}{x^{2} - 9 x + 14}$

Step 1

Factor $x^{2} - 9 x + 14$ 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 $14$ and whose sum is $- 9$ .

$- 7, - 2$

Step 1.2

Write the factored form using these integers.

$\frac{{(x - 7)}^{2}}{(x - 7) (x - 2)}$

Step 2

Cancel the common factor of ${(x - 7)}^{2}$ and $x - 7$ .

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Step 2.1

Factor $x - 7$ out of ${(x - 7)}^{2}$ .

$\frac{(x - 7) (x - 7)}{(x - 7) (x - 2)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Cancel the common factor.

$\frac{(x - 7) (x - 7)}{(x - 7) (x - 2)}$

Step 2.2.2

Rewrite the expression.

$\frac{x - 7}{x - 2}$