Algebra Examples

$\frac{\frac{8 x}{x^{2} - 1}}{\frac{10 x}{x + 1}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{8 x}{x^{2} - 1} \cdot \frac{x + 1}{10 x}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2 x$ .

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Step 2.1.1

Factor $2 x$ out of $8 x$ .

$\frac{2 x (4)}{x^{2} - 1} \cdot \frac{x + 1}{10 x}$

Step 2.1.2

Factor $2 x$ out of $10 x$ .

$\frac{2 x (4)}{x^{2} - 1} \cdot \frac{x + 1}{2 x (5)}$

Step 2.1.3

Cancel the common factor.

$\frac{2 x \cdot 4}{x^{2} - 1} \cdot \frac{x + 1}{2 x \cdot 5}$

Step 2.1.4

Rewrite the expression.

$\frac{4}{x^{2} - 1} \cdot \frac{x + 1}{5}$

Step 2.2

Multiply $\frac{4}{x^{2} - 1}$ by $\frac{x + 1}{5}$ .

$\frac{4 (x + 1)}{(x^{2} - 1) \cdot 5}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{4 (x + 1)}{(x^{2} - 1^{2}) \cdot 5}$

Step 3.2

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 $b = 1$ .

$\frac{4 (x + 1)}{(x + 1) (x - 1) \cdot 5}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $x + 1$ .

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Step 4.1.1

Cancel the common factor.

$\frac{4 (x + 1)}{(x + 1) (x - 1) \cdot 5}$

Step 4.1.2

Rewrite the expression.

$\frac{4}{(x - 1) \cdot 5}$

Step 4.2

Move $5$ to the left of $x - 1$ .

$\frac{4}{5 (x - 1)}$