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

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{1}{x}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $x$ by $1$ .

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

Step 4

Simplify the denominator.

Multiply $x$ by $x$ .

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

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

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

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

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

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

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

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

Factor $x$ out of $- x$ .

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

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

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

Step 5

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x}$