Algebra Examples

$\frac{1}{v - 4} \cdot \frac{v^{2} - 7 v + 12}{v + 3}$

Step 1

Factor $v^{2} - 7 v + 12$ 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 $12$ and whose sum is $- 7$ .

$- 4, - 3$

Step 1.2

Write the factored form using these integers.

$\frac{1}{v - 4} \cdot \frac{(v - 4) (v - 3)}{v + 3}$

Step 2

Cancel the common factor of $v - 4$ .

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Step 2.1

Cancel the common factor.

$\frac{1}{v - 4} \cdot \frac{(v - 4) (v - 3)}{v + 3}$

Step 2.2

Rewrite the expression.

$\frac{v - 3}{v + 3}$