Pre-Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Factor $2$ out of $2 a$ .

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

Step 1.2

Factor $2$ out of $2 b$ .

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

Step 1.3

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

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $a + b$ .

Tap for more steps...

Step 3.1.1

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

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

$\frac{2}{3} \cdot \frac{a - b}{a - b}$

Step 3.2

Multiply $\frac{2}{3}$ by $\frac{a - b}{a - b}$ .

$\frac{2 (a - b)}{3 (a - b)}$

Step 3.3

Cancel the common factor of $a - b$ .

Tap for more steps...

Step 3.3.1

Cancel the common factor.

$\frac{2 (a - b)}{3 (a - b)}$

Step 3.3.2

Rewrite the expression.

$\frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$