Question: Subtract. \[ \frac{7}{2} - \frac{9}{5x} \] Simplify your answer as much as possible.

Subtract.

\[ \frac{7}{2} - \frac{9}{5x} \]

Simplify your answer as much as possible.

Solution

To subtract the fractions \(\frac{7}{2}\) and \(\frac{9}{5x}\), we need a common denominator. First, identify the denominators: \(2\) and \(5x\). The common denominator is \(10x\). Rewrite each fraction with the common denominator: \[ \frac{7}{2} = \frac{7 \cdot 5x}{2 \cdot 5x} = \frac{35x}{10x} \] \[ \frac{9}{5x} = \frac{9 \cdot 2}{5x \cdot 2} = \frac{18}{10x} \] Now subtract the fractions: \[ \frac{35x}{10x} - \frac{18}{10x} = \frac{35x - 18}{10x} \] The expression \(\frac{35x - 18}{10x}\) is already simplified as much as possible. That is the final answer.