Basic Math Examples

$\frac{p^{2} - 16}{p^{2} - 13 p + 36}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$\frac{p^{2} - 4^{2}}{p^{2} - 13 p + 36}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = p$ and $b = 4$ .

$\frac{(p + 4) (p - 4)}{p^{2} - 13 p + 36}$

Step 2

Factor $p^{2} - 13 p + 36$ using the AC method.

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Step 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 $36$ and whose sum is $- 13$ .

$- 9, - 4$

Step 2.2

Write the factored form using these integers.

$\frac{(p + 4) (p - 4)}{(p - 9) (p - 4)}$

Step 3

Cancel the common factor of $p - 4$ .

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Step 3.1

Cancel the common factor.

$\frac{(p + 4) (p - 4)}{(p - 9) (p - 4)}$

Step 3.2

Rewrite the expression.

$\frac{p + 4}{p - 9}$