Pre-Algebra Examples

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

Step 1

Factor $3$ out of $3 a + 6 b$ .

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Step 1.1

Factor $3$ out of $3 a$ .

$\frac{3 (a) + 6 b}{a^{2} + 2 a b} \cdot \frac{a^{2}}{9}$

Step 1.2

Factor $3$ out of $6 b$ .

$\frac{3 (a) + 3 (2 b)}{a^{2} + 2 a b} \cdot \frac{a^{2}}{9}$

Step 1.3

Factor $3$ out of $3 (a) + 3 (2 b)$ .

$\frac{3 (a + 2 b)}{a^{2} + 2 a b} \cdot \frac{a^{2}}{9}$

Step 2

Factor $a$ out of $a^{2} + 2 a b$ .

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Step 2.1

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

$\frac{3 (a + 2 b)}{a \cdot a + 2 a b} \cdot \frac{a^{2}}{9}$

Step 2.2

Factor $a$ out of $2 a b$ .

$\frac{3 (a + 2 b)}{a \cdot a + a (2 b)} \cdot \frac{a^{2}}{9}$

Step 2.3

Factor $a$ out of $a \cdot a + a (2 b)$ .

$\frac{3 (a + 2 b)}{a (a + 2 b)} \cdot \frac{a^{2}}{9}$

Step 3

Combine.

$\frac{3 (a + 2 b) a^{2}}{a (a + 2 b) \cdot 9}$

Step 4

Cancel the common factor of $3$ and $9$ .

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Step 4.1

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

$\frac{3 ((a + 2 b) a^{2})}{a (a + 2 b) \cdot 9}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $a (a + 2 b) \cdot 9$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $a + 2 b$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{a^{2}}{a \cdot 3}$

Step 6

Cancel the common factor of $a^{2}$ and $a$ .

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Step 6.1

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

$\frac{a \cdot a}{a \cdot 3}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $a$ out of $a \cdot 3$ .

$\frac{a \cdot a}{a (3)}$

Step 6.2.2

Cancel the common factor.

$\frac{a \cdot a}{a \cdot 3}$

Step 6.2.3

Rewrite the expression.

$\frac{a}{3}$