Simplify ((2a+2b)/(a^2+ab))÷(4/a)

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

To divide by a fraction, multiply by its reciprocal.

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

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

Factor $2$ out of $2 a$ .

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

Factor $2$ out of $2 b$ .

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

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

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

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

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

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

Factor $a$ out of $a b$ .

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $a + b$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$