Q31. Find each product or quotient.3b... [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: Q31. (page 729)

Find each product or quotient.
$\frac{3 b 鈭� 12}{b + 4} 梅 (b^{2} 鈭� 6 b + 8)$

Short Answer

Expert verified

The simplified expression is $\frac{3}{b^{2} + 2 b 鈭� 8}$ .

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. Multiply by the reciprocal of b2−6b+8.

First multiply by the reciprocal of $b^{2} 鈭� 6 b + 8$ and then factor the expressions in numerator and denominator.

role="math" localid="1648050245885" $\frac{3 b 鈭� 12}{b + 4} 梅 (b^{2} 鈭� 6 b + 8) = \frac{3 b 鈭� 12}{b + 4} 脳 \frac{1}{b^{2} 鈭� 6 b + 8} = \frac{3 (b 鈭� 4)}{b + 4} 脳 \frac{1}{(b 鈭� 4) (b 鈭� 2)}$

Step 3. Simplify the expression.

Further simplify the expression by cancelling out the common factors $b 鈭� 4$ .

role="math" localid="1648050393663" $\begin{matrix} \frac{3 b 鈭� 12}{b + 4} 梅 (b^{2} 鈭� 6 b + 8) = \frac{3 (b 鈭� 4)}{b + 4} 脳 \frac{1}{(b 鈭� 4) (b 鈭� 2)} \\ = \frac{3}{(b + 4) (b 鈭� 2)} \\ = \frac{3}{b^{2} + 2 b 鈭� 8} \end{matrix}$

Therefore, the simplified expression is role="math" localid="1648050403311" $\frac{3}{b^{2} + 2 b 鈭� 8}$ .

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91影视

Find each product or quotient.
$\frac{3 b 鈭� 12}{b + 4} 梅 (b^{2} 鈭� 6 b + 8)$

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Multiply by the reciprocal of b2−6b+8.

Step 3. Simplify the expression.

One App. One Place for Learning.

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91影视

Find each product or quotient.3b鈭�12b+4梅b2鈭�6b+8

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Multiply by the reciprocal of b2−6b+8.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Find each product or quotient.
$\frac{3 b 鈭� 12}{b + 4} 梅 (b^{2} 鈭� 6 b + 8)$