Chapter 7: Q. 25 (page 651)

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

Short Answer

Expert verified

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

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 $\frac{w^{3} + 216}{w^{2} - 36} = \frac{(w + 6) (w^{2} + 6 w + 36)}{(w + 6) (w - 6)}, \sin c e w^{3} + 216 c a n f a c t o r i z e i n t h e f o r m o f a^{3} + b^{3} = a^{2} + a b + b^{2} = \frac{(w^{2} + 6 w + 36)}{(w - 6)}, w \neq 6, d i v i d e o u t t h e c o m m o n f a c t o r .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

. Given information

. Simplification of rational expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Simplify the rational expression w3+216w2-36

Short Answer

Step by step solution

. Given information

. Simplification of rational expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

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