Precalculus Examples

$1 - \frac{1}{1 - \frac{3}{x}}$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify the denominator.

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Step 1.1.1.1

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

$1 - \frac{1}{\frac{x}{x} - \frac{3}{x}}$

Step 1.1.1.2

Combine the numerators over the common denominator.

$1 - \frac{1}{\frac{x - 3}{x}}$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$1 - (1 \frac{x}{x - 3})$

Step 1.1.3

Multiply $\frac{x}{x - 3}$ by $1$ .

$1 - \frac{x}{x - 3}$

Step 1.2

Combine into one fraction.

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Step 1.2.1

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

$\frac{x - 3}{x - 3} - \frac{x}{x - 3}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{x - 3 - x}{x - 3}$

Step 2

Simplify the numerator.

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Step 2.1

Subtract $x$ from $x$ .

$\frac{0 - 3}{x - 3}$

Step 2.2

Subtract $3$ from $0$ .

$\frac{- 3}{x - 3}$

Step 3

Move the negative in front of the fraction.

$- \frac{3}{x - 3}$