Algebra Examples

$\frac{x + 3}{x + 2} \cdot \frac{2 x - 4}{x^{2} - 9}$

Step 1

Factor $2$ out of $2 x - 4$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $2 x$ .

$\frac{x + 3}{x + 2} \cdot \frac{2 (x) - 4}{x^{2} - 9}$

Step 1.2

Factor $2$ out of $- 4$ .

$\frac{x + 3}{x + 2} \cdot \frac{2 x + 2 \cdot - 2}{x^{2} - 9}$

Step 1.3

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

$\frac{x + 3}{x + 2} \cdot \frac{2 (x - 2)}{x^{2} - 9}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $9$ as $3^{2}$ .

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

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 $a = x$ and $b = 3$ .

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $x + 3$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

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

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