Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

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 $b = 1$ .

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

Step 2

Cancel the common factor of $x + 1$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Multiply $\frac{1}{x - 1} \cdot \frac{x}{x - 1}$ .

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Step 3.1

Multiply $\frac{1}{x - 1}$ by $\frac{x}{x - 1}$ .

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

Step 3.2

Raise $x - 1$ to the power of $1$ .

$\frac{x}{{(x - 1)}^{1} (x - 1)}$

Step 3.3

Raise $x - 1$ to the power of $1$ .

$\frac{x}{{(x - 1)}^{1} {(x - 1)}^{1}}$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x}{{(x - 1)}^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{x}{{(x - 1)}^{2}}$