Algebra Examples

$\frac{w^{2} + 5 w + 6}{w^{2} - w - 12}$

Step 1

Factor $w^{2} + 5 w + 6$ 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 $6$ and whose sum is $5$ .

$2, 3$

Step 1.2

Write the factored form using these integers.

$\frac{(w + 2) (w + 3)}{w^{2} - w - 12}$

Step 2

Factor $w^{2} - w - 12$ 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 $- 12$ and whose sum is $- 1$ .

$- 4, 3$

Step 2.2

Write the factored form using these integers.

$\frac{(w + 2) (w + 3)}{(w - 4) (w + 3)}$

Step 3

Cancel the common factor of $w + 3$ .

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Step 3.1

Cancel the common factor.

$\frac{(w + 2) (w + 3)}{(w - 4) (w + 3)}$

Step 3.2

Rewrite the expression.

$\frac{w + 2}{w - 4}$