Basic Math Examples

$\frac{b^{2} - 4}{6 b - 2} \cdot \frac{3 b - 1}{b^{2} - 2 b} \div (b + 2)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{b^{2} - 4}{6 b - 2} \cdot \frac{3 b - 1}{b^{2} - 2 b}}{b + 2}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{\frac{b^{2} - 2^{2}}{6 b - 2} \cdot \frac{3 b - 1}{b^{2} - 2 b}}{b + 2}$

Step 2.2

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

$\frac{\frac{(b + 2) (b - 2)}{6 b - 2} \cdot \frac{3 b - 1}{b^{2} - 2 b}}{b + 2}$

Step 3

Simplify with factoring out.

Tap for more steps...

Step 3.1

Factor $2$ out of $6 b - 2$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $6 b$ .

$\frac{\frac{(b + 2) (b - 2)}{2 (3 b) - 2} \cdot \frac{3 b - 1}{b^{2} - 2 b}}{b + 2}$

Step 3.1.2

Factor $2$ out of $- 2$ .

$\frac{\frac{(b + 2) (b - 2)}{2 (3 b) + 2 (- 1)} \cdot \frac{3 b - 1}{b^{2} - 2 b}}{b + 2}$

Step 3.1.3

Factor $2$ out of $2 (3 b) + 2 (- 1)$ .

$\frac{\frac{(b + 2) (b - 2)}{2 (3 b - 1)} \cdot \frac{3 b - 1}{b^{2} - 2 b}}{b + 2}$

Step 3.2

Factor $b$ out of $b^{2} - 2 b$ .

Tap for more steps...

Step 3.2.1

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

$\frac{\frac{(b + 2) (b - 2)}{2 (3 b - 1)} \cdot \frac{3 b - 1}{b \cdot b - 2 b}}{b + 2}$

Step 3.2.2

Factor $b$ out of $- 2 b$ .

$\frac{\frac{(b + 2) (b - 2)}{2 (3 b - 1)} \cdot \frac{3 b - 1}{b \cdot b + b \cdot - 2}}{b + 2}$

Step 3.2.3

Factor $b$ out of $b \cdot b + b \cdot - 2$ .

$\frac{\frac{(b + 2) (b - 2)}{2 (3 b - 1)} \cdot \frac{3 b - 1}{b (b - 2)}}{b + 2}$

Step 4

Multiply $\frac{(b + 2) (b - 2)}{2 (3 b - 1)}$ by $\frac{3 b - 1}{b (b - 2)}$ .

$\frac{\frac{(b + 2) (b - 2) (3 b - 1)}{2 (3 b - 1) (b (b - 2))}}{b + 2}$

Step 5

Remove unnecessary parentheses.

$\frac{\frac{(b + 2) (b - 2) (3 b - 1)}{2 (3 b - 1) b (b - 2)}}{b + 2}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Reduce the expression $\frac{(b + 2) (b - 2) (3 b - 1)}{2 (3 b - 1) b (b - 2)}$ by cancelling the common factors.

Tap for more steps...

Step 6.1.1

Cancel the common factor.

$\frac{\frac{(b + 2) (b - 2) (3 b - 1)}{2 (3 b - 1) b (b - 2)}}{b + 2}$

Step 6.1.2

Rewrite the expression.

$\frac{\frac{(b + 2) (3 b - 1)}{2 (3 b - 1) b}}{b + 2}$

Step 6.2

Cancel the common factor of $3 b - 1$ .

Tap for more steps...

Step 6.2.1

Cancel the common factor.

$\frac{\frac{(b + 2) (3 b - 1)}{2 (3 b - 1) b}}{b + 2}$

Step 6.2.2

Rewrite the expression.

$\frac{\frac{b + 2}{2 b}}{b + 2}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

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

Step 8

Cancel the common factor of $b + 2$ .

Tap for more steps...

Step 8.1

Cancel the common factor.

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

Step 8.2

Rewrite the expression.

$\frac{1}{2 b}$