Pre-Algebra Examples

$\frac{x^{2} + 3 x}{x^{2} + 6 x + 9}$

Step 1

Factor $x$ out of $x^{2} + 3 x$ .

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Step 1.1

Factor $x$ out of $x^{2}$ .

$\frac{x \cdot x + 3 x}{x^{2} + 6 x + 9}$

Step 1.2

Factor $x$ out of $3 x$ .

$\frac{x \cdot x + x \cdot 3}{x^{2} + 6 x + 9}$

Step 1.3

Factor $x$ out of $x \cdot x + x \cdot 3$ .

$\frac{x (x + 3)}{x^{2} + 6 x + 9}$

Step 2

Factor using the perfect square rule.

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Step 2.1

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

$\frac{x (x + 3)}{x^{2} + 6 x + 3^{2}}$

Step 2.2

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

$6 x = 2 \cdot x \cdot 3$

Step 2.3

Rewrite the polynomial.

$\frac{x (x + 3)}{x^{2} + 2 \cdot x \cdot 3 + 3^{2}}$

Step 2.4

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

$\frac{x (x + 3)}{{(x + 3)}^{2}}$

Step 3

Cancel the common factor of $x + 3$ and ${(x + 3)}^{2}$ .

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Step 3.1

Factor $x + 3$ out of $x (x + 3)$ .

$\frac{(x + 3) x}{{(x + 3)}^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{(x + 3) x}{(x + 3) (x + 3)}$

Step 3.2.2

Cancel the common factor.

$\frac{(x + 3) x}{(x + 3) (x + 3)}$

Step 3.2.3

Rewrite the expression.

$\frac{x}{x + 3}$