Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

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 $b = 1$ .

$\frac{4 x}{x - 1} \cdot \frac{(x + 1) (x - 1)}{3 x + 3}$

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{4 x}{x - 1} \cdot \frac{(x + 1) (x - 1)}{3 (x) + 3}$

Step 2.1.2

Factor $3$ out of $3$ .

$\frac{4 x}{x - 1} \cdot \frac{(x + 1) (x - 1)}{3 (x) + 3 (1)}$

Step 2.1.3

Factor $3$ out of $3 (x) + 3 (1)$ .

$\frac{4 x}{x - 1} \cdot \frac{(x + 1) (x - 1)}{3 (x + 1)}$

Step 2.2

Cancel the common factor of $x - 1$ .

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Step 2.2.1

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

$\frac{4 x}{x - 1} \cdot \frac{(x - 1) (x + 1)}{3 (x + 1)}$

Step 2.2.2

Cancel the common factor.

$\frac{4 x}{x - 1} \cdot \frac{(x - 1) (x + 1)}{3 (x + 1)}$

Step 2.2.3

Rewrite the expression.

$4 x \cdot \frac{x + 1}{3 (x + 1)}$

Step 2.3

Combine $4$ and $\frac{x + 1}{3 (x + 1)}$ .

$x \cdot \frac{4 (x + 1)}{3 (x + 1)}$

Step 2.4

Combine $x$ and $\frac{4 (x + 1)}{3 (x + 1)}$ .

$\frac{x (4 (x + 1))}{3 (x + 1)}$

Step 2.5

Cancel the common factor of $x + 1$ .

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Step 2.5.1

Cancel the common factor.

$\frac{x (4 (x + 1))}{3 (x + 1)}$

Step 2.5.2

Rewrite the expression.

$\frac{x \cdot (4)}{3}$

Step 2.6

Move $4$ to the left of $x$ .

$\frac{4 x}{3}$