Question

Simplify the rational expression $\frac{8m^{3}n}{12m{n}^2}$.

Short answer

The simplified form of rational expression$\frac{8m^{3}n}{12m{n}^2}$is$\frac{2m^2}{3n}$.

Step-by-step solution

Step 1. Given information

Given rational expression is $\frac{8m^{3}n}{12n^2}.$

we have to simplify the given rational expression.

. Simplification of rational expression

To simplify first we have to find out a common factor and divide out that common factor from both denominator and numerator and then simplify the rational expression.

so here common factor is 4mn , divide out from both numerator and denominator, then we get a simplified form

$$\begin{gathered} \frac{8m^{3}n}{12m{n}^2}=\frac{{\displaystyle \frac{8m^{3}n}{4mn}}}{{\displaystyle \frac{12m{n}^2}{4mn}}} \\ =\frac{2m^2}{3n} \end{gathered}$$