Basic Math Examples

$\frac{w^{2} + 6 w + 9}{12} \div (w + 3)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{w^{2} + 6 w + 9}{12}}{w + 3}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{w^{2} + 6 w + 9}{12} \cdot \frac{1}{w + 3}$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $9$ as $3^{2}$ .

$\frac{w^{2} + 6 w + 3^{2}}{12} \cdot \frac{1}{w + 3}$

Step 3.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 w = 2 \cdot w \cdot 3$

Step 3.3

Rewrite the polynomial.

$\frac{w^{2} + 2 \cdot w \cdot 3 + 3^{2}}{12} \cdot \frac{1}{w + 3}$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = w$ and $b = 3$ .

$\frac{{(w + 3)}^{2}}{12} \cdot \frac{1}{w + 3}$

Step 4

Cancel the common factor of $w + 3$ .

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Step 4.1

Factor $w + 3$ out of ${(w + 3)}^{2}$ .

$\frac{(w + 3) (w + 3)}{12} \cdot \frac{1}{w + 3}$

Step 4.2

Cancel the common factor.

$\frac{(w + 3) (w + 3)}{12} \cdot \frac{1}{w + 3}$

Step 4.3

Rewrite the expression.

$\frac{w + 3}{12}$