Question: Simplify. \(\frac{2}{5} \cdot \frac{1}{2} \cdot x \cdot x\) Assume that the variable…

Simplify.

\(\frac{2}{5} \cdot \frac{1}{2} \cdot x \cdot x\)

Assume that the variable represents a positive number.

Solution

The problem to simplify is \[ \frac{\frac{2}{5}}{x} \cdot \frac{1}{\frac{x}{2}} \] First, simplify the second fraction: \[ \frac{1}{\frac{x}{2}} = \frac{2}{x} \] Now replace it in the original expression: \[ \frac{\frac{2}{5}}{x} \cdot \frac{2}{x} \] Combine the two fractions: \[ \frac{2}{5x} \cdot \frac{2}{x} = \frac{2 \times 2}{5x \times x} \] Simplify the expression: \[ \frac{4}{5x^2} \] The simplified expression is \[ \frac{4}{5x^2} \]