Question

Simplify the expression. $$\frac{3 x^{2}}{10} \div \frac{9 x^{3}}{25}$$

Short answer

The simplified expression is \( \frac{5}{6x} \).

Step-by-step solution

Rewrite Division as Multiplication

The expression can be rewritten as \(\frac{3 x^{2}}{10} * \frac{25}{9 x^{3}}\) by reciprocating the second fraction.

Multiply Fractions

Perform multiplication between the fractions. Multiply the numerators together to form the new numerator and the denominators to form the new denominator getting \(\frac{75 x^{2}}{90 x^{3}}\).

Simplify the Expression

Simplify the expression by cancelling out the common factors between the numerator and denominator. We get \(\frac{75 x^{2}}{90 x^{3}} = \frac{5}{6x}\) by cancelling \(15x^{2}\) out of the numerator and denominator and simplifying.