Question

Simplify the rational expression $\frac{36v^3{w}^2}{27v{w}^3}.$

Short answer

Simplified form of the given rational expression is$\frac{4v^2}{3w}$.

Step-by-step solution

Step 1. Given information

Given rational expression is $\frac{36v^3{w}^2}{27v{w}^3}.$

We have to simplify the given rational expression.

Step 2. Simplification of the rational expression

To simplify , first we have to find out common factor and divide out from both numerator and denominator, then we get the simplified form of the expression.

Here common factor is $9v{w}^2$, then the simplified form of the given rational expression becomes $$\begin{gathered} \frac{36v^3{w}^2}{27v{w}^3}=\frac{{\displaystyle \frac{36v^3{w}^2}{9v{w}^2}}}{{\displaystyle \frac{27v{w}^3}{9v{w}^2}}} \\ =\frac{4v^2}{3w} \end{gathered}$$