Chapter 11: Q30. (page 729)

Find each product or quotient.
$\frac{x^{2}}{x + 4} \div \frac{3 x}{x^{2} - 16}$

Short Answer

Expert verified

The simplified expression is $\frac{x^{2} - 4 x}{3}$ .

Step by step solution

Step 1. Define the concept.

Multiplying rational expression: - Let a, b, c, and d be polynomials with $b \neq 0$ and $d \neq 0$ . Then $\frac{a}{b} \cdot \frac{c}{d} = \frac{a c}{b d}$ .

Dividing rational expression: - Let a, b, c, and d be polynomials with $b \neq 0$ , $c \neq 0$ and $d \neq 0$ . Then $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{a d}{b c}$ .

Step 2. Multiply by the reciprocal of 3xx2−16.

First multiply by the reciprocal of $\frac{3 x}{x^{2} - 16}$ and then factor the expressions in numerator and denominator.

role="math" localid="1648049221815" $\frac{x^{2}}{x + 4} \div \frac{3 x}{x^{2} - 16} = \frac{x^{2}}{x + 4} \times \frac{x^{2} - 16}{3 x} = \frac{x^{2}}{x + 4} \times \frac{(x + 4) (x - 4)}{3 x}$

Step 3. Simplify the expression.

Further simplify the expression by cancelling out the common factors $x + 4$ and x.

role="math" localid="1648049342460" $\begin{matrix} \frac{x^{2}}{x + 4} \div \frac{3 x}{x^{2} - 16} = \frac{x \times x}{x + 4} \times \frac{(x + 4) (x - 4)}{3 x} \\ = \frac{x (x - 4)}{3} \\ = \frac{x^{2} - 4 x}{3} \end{matrix}$

Therefore, the simplified expression is $\frac{x^{2} - 4 x}{3}$ .

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.

Find each product or quotient.
$\frac{x^{2}}{x + 4} \div \frac{3 x}{x^{2} - 16}$

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Multiply by the reciprocal of 3xx2−16.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find each product or quotient.x2x+4÷3xx2−16

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Multiply by the reciprocal of 3xx2−16.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find each product or quotient.
$\frac{x^{2}}{x + 4} \div \frac{3 x}{x^{2} - 16}$