Algebra Examples

$\frac{6 a}{x^{2} - x} \cdot \frac{2 x - 2}{3 a x}$

Step 1

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

Tap for more steps...

Step 1.1

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

$\frac{6 a}{x \cdot x - x} \cdot \frac{2 x - 2}{3 a x}$

Step 1.2

Factor $x$ out of $- x$ .

$\frac{6 a}{x \cdot x + x \cdot - 1} \cdot \frac{2 x - 2}{3 a x}$

Step 1.3

Factor $x$ out of $x \cdot x + x \cdot - 1$ .

$\frac{6 a}{x (x - 1)} \cdot \frac{2 x - 2}{3 a x}$

Step 2

Factor $2$ out of $2 x - 2$ .

Tap for more steps...

Step 2.1

Factor $2$ out of $2 x$ .

$\frac{6 a}{x (x - 1)} \cdot \frac{2 (x) - 2}{3 a x}$

Step 2.2

Factor $2$ out of $- 2$ .

$\frac{6 a}{x (x - 1)} \cdot \frac{2 (x) + 2 (- 1)}{3 a x}$

Step 2.3

Factor $2$ out of $2 (x) + 2 (- 1)$ .

$\frac{6 a}{x (x - 1)} \cdot \frac{2 (x - 1)}{3 a x}$

Step 3

Cancel the common factor of $3 a$ .

Tap for more steps...

Step 3.1

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

$\frac{3 a (2)}{x (x - 1)} \cdot \frac{2 (x - 1)}{3 a x}$

Step 3.2

Factor $3 a$ out of $3 a x$ .

$\frac{3 a (2)}{x (x - 1)} \cdot \frac{2 (x - 1)}{3 a (x)}$

Step 3.3

Cancel the common factor.

$\frac{3 a \cdot 2}{x (x - 1)} \cdot \frac{2 (x - 1)}{3 a x}$

Step 3.4

Rewrite the expression.

$\frac{2}{x (x - 1)} \cdot \frac{2 (x - 1)}{x}$

Step 4

Cancel the common factor of $x - 1$ .

Tap for more steps...

Step 4.1

Factor $x - 1$ out of $x (x - 1)$ .

$\frac{2}{(x - 1) x} \cdot \frac{2 (x - 1)}{x}$

Step 4.2

Factor $x - 1$ out of $2 (x - 1)$ .

$\frac{2}{(x - 1) x} \cdot \frac{(x - 1) \cdot 2}{x}$

Step 4.3

Cancel the common factor.

$\frac{2}{(x - 1) x} \cdot \frac{(x - 1) \cdot 2}{x}$

Step 4.4

Rewrite the expression.

$\frac{2}{x} \cdot \frac{2}{x}$

Step 5

Multiply $\frac{2}{x}$ by $\frac{2}{x}$ .

$\frac{2 \cdot 2}{x \cdot x}$

Step 6

Multiply $2$ by $2$ .

$\frac{4}{x \cdot x}$

Step 7

Raise $x$ to the power of $1$ .

$\frac{4}{x^{1} x}$

Step 8

Raise $x$ to the power of $1$ .

$\frac{4}{x^{1} x^{1}}$

Step 9

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{x^{1 + 1}}$

Step 10

Add $1$ and $1$ .

$\frac{4}{x^{2}}$