Q 112. Divide Rational Expressions:聽v3... [FREE SOLUTION]

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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 112. (page 931)

Divide Rational Expressions: $\frac{v^{3} 鈥� 鈭� 鈥� 8 w^{3}}{2 v^{2} 鈥� + 鈥� 4 v w 鈥� + 鈥� 8 w^{2}} 梅 \frac{v^{2} 鈥� 鈭� 鈥� 4 w^{2}}{4}$

Short Answer

Expert verified

The required answer is $\frac{2}{v + 2 w}$ .

Step by step solution

Step 1. Given information.

The given expression is $\frac{v^{3} 鈥� 鈭� 鈥� 8 w^{3}}{2 v^{2} 鈥� + 鈥� 4 v w 鈥� + 鈥� 8 w^{2}} 梅 \frac{v^{2} 鈥� 鈭� 鈥� 4 w^{2}}{4}$ .

Step 2. Simplify the expression.

$\frac{v^{3} 鈥� 鈭� 鈥� 8 w^{3}}{2 v^{2} 鈥� + 鈥� 4 v w 鈥� + 鈥� 8 w^{2}} 梅 \frac{v^{2} 鈥� 鈭� 鈥� 4 w^{2}}{4} = \frac{\frac{v^{3} - 8 w^{3}}{2 v^{2} + 4 v w + 8 w^{2}}}{\frac{v^{2} - 4 w^{2}}{4}}$

Apply the fraction rule.

$\frac{(v^{3} - 8 w^{3}) 路鈥� 4}{(2 v^{2} + 4 v w + 8 w^{2}) (v^{2} - 4 w^{2})} = \frac{(v^{3} - 8 w^{3}) 路鈥� 4}{2 (v^{2} + 2 w v + 4 w^{2}) (v^{2} - 4 w^{2})} = \frac{(v^{3} - 8 w^{3}) 路鈥� 2 路鈥� 2}{2 (v^{2} + 2 w v + 4 w^{2}) (v^{2} - 4 w^{2})} = \frac{(v^{3} - 8 w^{3}) 路鈥� 2}{(v^{2} + 2 w v + 4 w^{2}) (v^{2} - 4 w^{2})}$

Step 3. Factor the numerators and denominators and then multiply.

$\frac{(v - 2 w) (v^{2} + 2 w v + 4 w^{2}) 路鈥� 2}{(v^{2} + 2 w v + 4 w^{2}) (v^{2} - 4 w^{2})} = \frac{(v - 2 w) 路鈥� 2}{v^{2} - 4 w^{2}} = \frac{(v - 2 w) 路鈥� 2}{(v + 2 w) (v - 2 w)} = \frac{2}{v + 2 w}$

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91影视

Divide Rational Expressions: $\frac{v^{3} 鈥� 鈭� 鈥� 8 w^{3}}{2 v^{2} 鈥� + 鈥� 4 v w 鈥� + 鈥� 8 w^{2}} 梅 \frac{v^{2} 鈥� 鈭� 鈥� 4 w^{2}}{4}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Factor the numerators and denominators and then multiply.

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Divide Rational Expressions:v3鈥�鈭�鈥�8w32v2鈥�+鈥�4vw鈥�+鈥�8w2梅v2鈥�鈭�鈥�4w24

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Factor the numerators and denominators and then multiply.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Calculus

Study anywhere. Anytime. Across all devices.

Divide Rational Expressions: $\frac{v^{3} 鈥� 鈭� 鈥� 8 w^{3}}{2 v^{2} 鈥� + 鈥� 4 v w 鈥� + 鈥� 8 w^{2}} 梅 \frac{v^{2} 鈥� 鈭� 鈥� 4 w^{2}}{4}$