Algebra Examples

$\frac{x^{2} - 4}{5 x} \cdot \frac{30}{3 x - 6}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

$\frac{x^{2} - 2^{2}}{5 x} \cdot \frac{30}{3 x - 6}$

Step 1.2

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

$\frac{(x + 2) (x - 2)}{5 x} \cdot \frac{30}{3 x - 6}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Factor $3$ out of $3 x - 6$ .

Tap for more steps...

Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{(x + 2) (x - 2)}{5 x} \cdot \frac{30}{3 (x) - 6}$

Step 2.1.2

Factor $3$ out of $- 6$ .

$\frac{(x + 2) (x - 2)}{5 x} \cdot \frac{30}{3 x + 3 \cdot - 2}$

Step 2.1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{(x + 2) (x - 2)}{5 x} \cdot \frac{30}{3 (x - 2)}$

Step 2.2

Cancel the common factor of $x - 2$ .

Tap for more steps...

Step 2.2.1

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

$\frac{(x - 2) (x + 2)}{5 x} \cdot \frac{30}{3 (x - 2)}$

Step 2.2.2

Factor $x - 2$ out of $3 (x - 2)$ .

$\frac{(x - 2) (x + 2)}{5 x} \cdot \frac{30}{(x - 2) \cdot 3}$

Step 2.2.3

Cancel the common factor.

$\frac{(x - 2) (x + 2)}{5 x} \cdot \frac{30}{(x - 2) \cdot 3}$

Step 2.2.4

Rewrite the expression.

$\frac{x + 2}{5 x} \cdot \frac{30}{3}$

Step 2.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.3.1

Factor $5$ out of $5 x$ .

$\frac{x + 2}{5 (x)} \cdot \frac{30}{3}$

Step 2.3.2

Factor $5$ out of $30$ .

$\frac{x + 2}{5 (x)} \cdot \frac{5 (6)}{3}$

Step 2.3.3

Cancel the common factor.

$\frac{x + 2}{5 x} \cdot \frac{5 \cdot 6}{3}$

Step 2.3.4

Rewrite the expression.

$\frac{x + 2}{x} \cdot \frac{6}{3}$

Step 2.4

Multiply $\frac{x + 2}{x}$ by $\frac{6}{3}$ .

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

Step 2.5

Cancel the common factor of $6$ and $3$ .

Tap for more steps...

Step 2.5.1

Factor $3$ out of $(x + 2) \cdot 6$ .

$\frac{3 ((x + 2) \cdot 2)}{x \cdot 3}$

Step 2.5.2

Cancel the common factors.

Tap for more steps...

Step 2.5.2.1

Factor $3$ out of $x \cdot 3$ .

$\frac{3 ((x + 2) \cdot 2)}{3 \cdot x}$

Step 2.5.2.2

Cancel the common factor.

$\frac{3 ((x + 2) \cdot 2)}{3 \cdot x}$

Step 2.5.2.3

Rewrite the expression.

$\frac{(x + 2) \cdot 2}{x}$

Step 2.6

Move $2$ to the left of $x + 2$ .

$\frac{2 (x + 2)}{x}$