Basic Math Examples

$\frac{w^{2} - 2 w - 63}{w^{2} + 10 w + 21}$

Step 1

Factor $w^{2} - 2 w - 63$ 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 $- 63$ and whose sum is $- 2$ .

$- 9, 7$

Step 1.2

Write the factored form using these integers.

$\frac{(w - 9) (w + 7)}{w^{2} + 10 w + 21}$

Step 2

Factor $w^{2} + 10 w + 21$ 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 $21$ and whose sum is $10$ .

$3, 7$

Step 2.2

Write the factored form using these integers.

$\frac{(w - 9) (w + 7)}{(w + 3) (w + 7)}$

Step 3

Cancel the common factor of $w + 7$ .

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Step 3.1

Cancel the common factor.

$\frac{(w - 9) (w + 7)}{(w + 3) (w + 7)}$

Step 3.2

Rewrite the expression.

$\frac{w - 9}{w + 3}$