Question

Operations with Algebraic Expressions Perform the indicated operations and simplify.

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

Short answer

The simplified form of the given expression is $-\frac{1}{2x}$.

Step-by-step solution

Step 1. Property of fractions.

To divide a fraction by another fraction, we invert the divisor and multiply.

$\frac{A}{B}÷\frac{C}{D}=\frac{A}{B}\times \frac{D}{C}$

Step 2. Given Information.

The given expression is:

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

Step 3. Simplify the given expression.

The given expression can be rewritten as:

$\begin{array}{c}\frac{\frac{1}{x}-\frac{1}{2}}{x-2}=\frac{\frac{2-x}{2x}}{x-2}\\ =\frac{2-x}{2x}\times \frac{1}{x-2}\\ =\frac{-(x-2)}{2x}\times \frac{1}{x-2}\\ =-\frac{1}{2x}\end{array}$

Thus, the simplified form of the given expression is $-\frac{1}{2x}$.