Chapter 11: Q31. (page 729)

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

Short Answer

Expert verified

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

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 b2−6b+8.

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

role="math" localid="1648050245885" $\frac{3 b - 12}{b + 4} \div (b^{2} - 6 b + 8) = \frac{3 b - 12}{b + 4} \times \frac{1}{b^{2} - 6 b + 8} = \frac{3 (b - 4)}{b + 4} \times \frac{1}{(b - 4) (b - 2)}$

Step 3. Simplify the expression.

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

role="math" localid="1648050393663" $\begin{matrix} \frac{3 b - 12}{b + 4} \div (b^{2} - 6 b + 8) = \frac{3 (b - 4)}{b + 4} \times \frac{1}{(b - 4) (b - 2)} \\ = \frac{3}{(b + 4) (b - 2)} \\ = \frac{3}{b^{2} + 2 b - 8} \end{matrix}$

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

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

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.

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Find each product or quotient.3b−12b+4÷b2−6b+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

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Mechanics Maths

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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