Q29. Find each product or quotient.3x... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q29. (page 729)

Find each product or quotient.
$\frac{3 x 鈭� 6}{x^{2} 鈭� 9} 鈰� \frac{x + 3}{x^{2} 鈭� 2 x}$

Short Answer

Expert verified

The final product of the expression is $\frac{3}{x (x 鈭� 3)}$ .

Step by step solution

Step 1. Define the concept.

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

Dividing rational expression: - Let a, b, c, and d be polynomials with $b 鈮� 0$ , $c 鈮� 0$ and $d 鈮� 0$ . Then $\frac{a}{b} 梅 \frac{c}{d} = \frac{a}{b} 鈰� \frac{d}{c} = \frac{a d}{b c}$ .

Step 2. Divide by the common factors before multiplying.

First factor the numerator and denominator of both the rational expressions.

$\frac{3 x 鈭� 6}{x^{2} 鈭� 9} 鈰� \frac{x + 3}{x^{2} 鈭� 2 x} = \frac{3 (x 鈭� 2)}{(x 鈭� 3) (x + 3)} 鈰� \frac{x + 3}{x (x 鈭� 2)}$

Step 3. Simplify the expression.

Further simplify the expression by dividing by the common factors $x - 2$ , and $x + 3$ .

role="math" localid="1648048255063" $\begin{matrix} \frac{3 x 鈭� 6}{x^{2} 鈭� 9} 鈰� \frac{x + 3}{x^{2} 鈭� 2 x} = \frac{3 (x 鈭� 2)}{(x 鈭� 3) (x + 3)} 鈰� \frac{x + 3}{x (x 鈭� 2)} \\ = \frac{3}{x 鈭� 3} 鈰� \frac{1}{x} \\ = \frac{3}{x (x 鈭� 3)} \end{matrix}$

Therefore, the final product of the expression is $\frac{3}{x (x 鈭� 3)}$ .

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91影视

Find each product or quotient.
$\frac{3 x 鈭� 6}{x^{2} 鈭� 9} 鈰� \frac{x + 3}{x^{2} 鈭� 2 x}$

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Divide by the common factors before multiplying.

Step 3. Simplify the expression.

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91影视

Find each product or quotient.3x鈭�6x2鈭�9鈰�x+3x2鈭�2x

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Divide by the common factors before multiplying.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find each product or quotient.
$\frac{3 x 鈭� 6}{x^{2} 鈭� 9} 鈰� \frac{x + 3}{x^{2} 鈭� 2 x}$