Question

Simplify the expression. $$\frac{8 x^{2}}{3} \cdot \frac{9}{16 x}$$

Short answer

The simplification of the given expression results in \(\frac{3x}{2}\).

Step-by-step solution

Write Out the Expression

Rewrite the given expression. With it:\[\frac{8 x^{2}}{3} \cdot \frac{9}{16 x}\] the aim is to simplify it as much as possible using the standard rules of computation for rational expressions.

Simplify by Multiplication

Rewrite the expression by multiplying the numerators together and the denominators together: \[\frac{8 x^{2}\cdot 9}{3\cdot 16 x}\] simplifying further produces the expression \[\frac{72x^2}{48x}\].

Simplify by Cancelling

Next, simplify the expression by cancelling out common terms in the numerator and denominator. In this case, one 'x' in the numerator and the 'x' in the denominator can cancel out, and the coefficient can be simplified by dividing both the numerator and denominator by their greatest common factor (24 in this case) providing a simplified expression of \[\frac{3x}{2}\].