Algebra Examples

$\frac{2 a + 2 b}{a^{2} + a b} \div \frac{4}{a}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 a + 2 b}{a^{2} + a b} \cdot \frac{a}{4}$

Step 2

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

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Step 2.1

Factor $2$ out of $2 a$ .

$\frac{2 (a) + 2 b}{a^{2} + a b} \cdot \frac{a}{4}$

Step 2.2

Factor $2$ out of $2 b$ .

$\frac{2 (a) + 2 (b)}{a^{2} + a b} \cdot \frac{a}{4}$

Step 2.3

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

$\frac{2 (a + b)}{a^{2} + a b} \cdot \frac{a}{4}$

Step 3

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

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Step 3.1

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

$\frac{2 (a + b)}{a \cdot a + a b} \cdot \frac{a}{4}$

Step 3.2

Factor $a$ out of $a b$ .

$\frac{2 (a + b)}{a \cdot a + a (b)} \cdot \frac{a}{4}$

Step 3.3

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

$\frac{2 (a + b)}{a (a + b)} \cdot \frac{a}{4}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $4$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $a$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{a + b}{a + b} \cdot \frac{1}{2}$

Step 6

Multiply $\frac{a + b}{a + b}$ by $\frac{1}{2}$ .

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

Step 7

Cancel the common factor of $a + b$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

$\frac{1}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$