Basic Math Examples

$\frac{v^{2} - 14 v + 45}{v^{2} - 1}$

Step 1

Factor $v^{2} - 14 v + 45$ 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 $45$ and whose sum is $- 14$ .

$- 9, - 5$

Step 1.2

Write the factored form using these integers.

$\frac{(v - 9) (v - 5)}{v^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{(v - 9) (v - 5)}{v^{2} - 1^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = v$ and $b = 1$ .

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