Question

Simplify the expression. $$\frac{9}{5 x}-\frac{2}{x^{2}}$$

Short answer

The simplified form of the expression is \(\frac{9x-10}{5x^2}\).

Step-by-step solution

Identifying the denominators

First, identify that the denominators are \(5x\) and \(x^2\).

Find the least common denominator

The least common denominator of \(5x\) and \(x^2\) is \(5x^2\).

Rewrite fractions with common denominator

Next, rewrite the fractions to have the same common denominator. Multiply \(\frac{9}{5x}\) by \(\frac{x}{x}\) and \(\frac{2}{x^2}\) by \(\frac{5}{5}\) yielding \(\frac{9x}{5x^2}-\frac{10}{5x^2}\).

Simplify the expression

Finally, simplify the expression by combining the fractions, which gives us \(\frac{9x-10}{5x^2}\).