Finite Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Write $1$ as a fraction with a common denominator.

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Rewrite $\frac{x - 1 + 1}{x - 1}$ in a factored form.

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Step 1.3.1

Add $- 1$ and $1$ .

$\frac{x}{1 - \frac{1}{\frac{x + 0}{x - 1}}}$

Step 1.3.2

Add $x$ and $0$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.2

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

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

Step 2.3

Write $1$ as a fraction with a common denominator.

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Rewrite $\frac{x - (x - 1)}{x}$ in a factored form.

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Step 2.5.1

Apply the distributive property.

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

Step 2.5.2

Multiply $- 1$ by $- 1$ .

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

Step 2.5.3

Subtract $x$ from $x$ .

$\frac{x}{\frac{0 + 1}{x}}$

Step 2.5.4

Add $0$ and $1$ .

$\frac{x}{\frac{1}{x}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$x \cdot x$

Step 4

Multiply $x$ by $x$ .

$x^{2}$