Calculus Examples

$\frac{x + 8}{x^{2} - x - 72}$

Step 1

Factor $x^{2} - x - 72$ 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 $- 72$ and whose sum is $- 1$ .

$- 9, 8$

Step 1.2

Write the factored form using these integers.

$\frac{x + 8}{(x - 9) (x + 8)}$

Step 2

Cancel the common factor of $x + 8$ .

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Step 2.1

Cancel the common factor.

$\frac{x + 8}{(x - 9) (x + 8)}$

Step 2.2

Rewrite the expression.

$\frac{1}{x - 9}$