Question

Simplify the rational expression $\frac{w^3+216}{w^2-36}$

Short answer

Simplified form of rational expression$\frac{w^3+216}{w^2-36}is\frac{(w^2-6w+36)}{w-6},w\ne 6$

Step-by-step solution

. Given information

Given rational expression is $\frac{w^3+216}{w^2-36}$.

We need to simplify the rational expression.

. Simplification of rational expression

To simplify first we need to factor both numerator and denominator and find out the common factor , then simplify the expression.

Thus simplified form of expression is$$\begin{gathered} \frac{w^3+216}{w^2-36}=\frac{(w+6)(w^2+6w+36)}{(w+6)(w-6)},\sin ce{w}^3+216canfactorizeintheformof{a}^3+b^3=a^2+ab+b^2 \\ =\frac{(w^2+6w+36)}{(w-6)},w\ne 6,divideoutthecommonfactor. \end{gathered}$$