Algebra Examples

$\frac{x + 1}{3 x + 6} \cdot \frac{6 x + 12}{x^{2} - 1}$

Step 1

Simplify with factoring out.

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Step 1.1

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

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{x + 1}{3 (x) + 6} \cdot \frac{6 x + 12}{x^{2} - 1}$

Step 1.1.2

Factor $3$ out of $6$ .

$\frac{x + 1}{3 x + 3 \cdot 2} \cdot \frac{6 x + 12}{x^{2} - 1}$

Step 1.1.3

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

$\frac{x + 1}{3 (x + 2)} \cdot \frac{6 x + 12}{x^{2} - 1}$

Step 1.2

Factor $6$ out of $6 x + 12$ .

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Step 1.2.1

Factor $6$ out of $6 x$ .

$\frac{x + 1}{3 (x + 2)} \cdot \frac{6 (x) + 12}{x^{2} - 1}$

Step 1.2.2

Factor $6$ out of $12$ .

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

Step 1.2.3

Factor $6$ out of $6 x + 6 \cdot 2$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

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

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 $b = 1$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x + 1$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $3 (x + 2)$ .

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{2}{x - 1}$