Algebra Examples

$\frac{x + 6}{x^{2} - x - 42}$

Step 1

Factor $x^{2} - x - 42$ 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 $- 42$ and whose sum is $- 1$ .

$- 7, 6$

Step 1.2

Write the factored form using these integers.

$\frac{x + 6}{(x - 7) (x + 6)}$

Step 2

Cancel the common factor of $x + 6$ .

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Step 2.1

Cancel the common factor.

$\frac{x + 6}{(x - 7) (x + 6)}$

Step 2.2

Rewrite the expression.

$\frac{1}{x - 7}$