Chapter 11: Q24. (page 728)

Simplify each expression.
$\frac{3 x^{3}}{3 x^{3} + 6 x^{2}}$

Short Answer

Expert verified

The simplified expression is $\frac{x}{x + 2}$ .

Step by step solution

Step 1. Define rational expression.

A rational expression is an algebraic expression whose numerator and denominator are polynomials. Also, division by 0 is undefined, so therefore, the polynomials in the denominator cannot be zero and the values for which the denominator is zero is termed as excluded values for the respective rational expression.

Step 2. Factor the expression.

Factor the numerator and denominator, using their greatest common factor in the expression $\frac{3 x^{3}}{3 x^{3} + 6 x^{2}}$ .

$\frac{3 x^{3}}{3 x^{3} + 6 x^{2}} = \frac{3 x^{2} (x)}{3 x^{2} (x + 2)}$

Step 3. Simplify the expression.

Further simplify the expression.

$\frac{3 x^{3}}{3 x^{3} + 6 x^{2}} = \frac{3 x^{2} (x)}{3 x^{2} (x + 2)} = \frac{x}{x + 2}$

Therefore, the simplified expression is $\frac{x}{x + 2}$ .

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 each expression.
$\frac{3 x^{3}}{3 x^{3} + 6 x^{2}}$

Short Answer

Step by step solution

Step 1. Define rational expression.

Step 2. Factor the expression.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Decision Maths

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify each expression.3x33x3+6x2

Short Answer

Step by step solution

Step 1. Define rational expression.

Step 2. Factor the expression.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Decision Maths

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify each expression.
$\frac{3 x^{3}}{3 x^{3} + 6 x^{2}}$