Simplify (1/x-1)/(x-1)

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

Step 1

Multiply the numerator and denominator of the complex fraction by $x$ .

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Step 5

Simplify the denominator.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Factor $x$ out of $x^{2} - x$ .

Factor $x$ out of $x^{2}$ .

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

Factor $x$ out of $- x$ .

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

Factor $x$ out of $x \cdot x + x \cdot - 1$ .

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

Step 6

Reduce the expression by cancelling the common factors.

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

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

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

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

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1}{x}$

Move the negative in front of the fraction.

$- \frac{1}{x}$

Simplify (1/x-1)/(x-1)

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