Simplify (x/2-1)/(x-2)

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

Step 1

Multiply the numerator and denominator of the complex fraction by $2$ .

Multiply $\frac{\frac{x}{2} - 1}{x - 2}$ by $\frac{2}{2}$ .

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

Combine.

$\frac{2 (\frac{x}{2} - 1)}{2 (x - 2)}$

Step 2

Apply the distributive property.

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

Step 3

Simplify terms.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 1$ .

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

Factor $2$ out of $2 x + 2 \cdot - 2$ .

Factor $2$ out of $2 x$ .

$\frac{x - 2}{2 (x) + 2 \cdot - 2}$

Factor $2$ out of $2 \cdot - 2$ .

$\frac{x - 2}{2 (x) + 2 (- 2)}$

Factor $2$ out of $2 (x) + 2 (- 2)$ .

$\frac{x - 2}{2 (x - 2)}$

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{x - 2}{2 (x - 2)}$

Rewrite the expression.

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$