Finite Math Examples

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

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

Step 1

Simplify the denominator.

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Step 1.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2

Combine the numerators over the common denominator.

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

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

Step 1.3

Rewrite

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

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

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Step 1.3.1

Add

- 1

$- 1$ and

1

$1$ .

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

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

Step 1.3.2

Add

x

$x$ and

0

$0$ .

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

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

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

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

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

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

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})}

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

Step 2.2

Multiply

\frac{x - 1}{x}

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

1

$1$ .

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

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

Step 2.3

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 2.4

Combine the numerators over the common denominator.

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

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

Step 2.5

Rewrite

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

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

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Step 2.5.1

Apply the distributive property.

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

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

Step 2.5.2

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

Step 2.5.3

Subtract

x

$x$ from

x

$x$ .

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

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

Step 2.5.4

Add

0

$0$ and

1

$1$ .

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

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

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

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

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

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

x \cdot x

$x \cdot x$

Step 4

Multiply

x

$x$ by

x

$x$ .

x^{2}

$x^{2}$