Finite Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Reorder terms.

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

Step 1.4

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

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Step 1.4.1

Subtract $1$ from $1$ .

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

Step 1.4.2

Add $- x$ and $0$ .

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

Step 1.5

Move the negative in front of the fraction.

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

Step 2

Cancel the common factor of $1$ and $- 1$ .

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Step 2.1

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 2.2

Move the negative in front of the fraction.

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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

Step 5

Factor $- 1$ out of $- x$ .

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

Step 6

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 7

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

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

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (x - 1)$ as $- 1 (x - 1)$ .

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

Step 8.2

Move the negative in front of the fraction.

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

Step 9

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x$

Step 10

The LCM of one and any expression is the expression.

$x$