Q 109. Divide Rational Expressions:聽3s... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 109. (page 931)

Divide Rational Expressions: $\frac{3 s^{2}}{s^{2} 鈥� 鈭� 鈥� 16} 梅 \frac{s^{3} 鈥� + 鈥� 4 s^{2} 鈥� + 鈥� 16 s}{s^{3} 鈥� 鈭� 鈥� 64}$ .

Short Answer

Expert verified

The required answer is $\frac{3 s}{s + 4}$ .

Step by step solution

Step 1. Given information.

The given expression is $鈥� 鈥� \frac{3 s^{2}}{s^{2} 鈥� 鈭� 鈥� 16} 梅 \frac{s^{3} 鈥� + 鈥� 4 s^{2} 鈥� + 鈥� 16 s}{s^{3} 鈥� 鈭� 鈥� 64}$ .

Step 2. Simplify the expression.

$鈥� 鈥� \frac{3 s^{2}}{s^{2} 鈥� 鈭� 鈥� 16} 梅 \frac{s^{3} 鈥� + 鈥� 4 s^{2} 鈥� + 鈥� 16 s}{s^{3} 鈥� 鈭� 鈥� 64} = \frac{\frac{3 s^{2}}{s^{2} - 16}}{\frac{s^{3} + 4 s^{2} + 16 s}{s^{3} - 64}}$

Apply the fraction rule.

$= \frac{3 s^{2} (s^{3} - 64)}{(s^{2} - 16) (s^{3} + 4 s^{2} + 16 s)} = \frac{3 s s (s^{3} - 64)}{(s^{2} - 16) s (s^{2} + 4 s + 16)} = \frac{3 s (s - 4) (s^{2} + 4 s + 16)}{(s^{2} - 16) (s^{2} + 4 s + 16)} = \frac{3 s (s - 4)}{s^{2} - 16} = \frac{3 s (s - 4)}{(s + 4) (s - 4)} = \frac{3 s}{s + 4}$

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91影视

Divide Rational Expressions: $\frac{3 s^{2}}{s^{2} 鈥� 鈭� 鈥� 16} 梅 \frac{s^{3} 鈥� + 鈥� 4 s^{2} 鈥� + 鈥� 16 s}{s^{3} 鈥� 鈭� 鈥� 64}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

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91影视

Divide Rational Expressions:3s2s2鈥�鈭�鈥�16梅s3鈥�+鈥�4s2鈥�+鈥�16ss3鈥�鈭�鈥�64.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Divide Rational Expressions: $\frac{3 s^{2}}{s^{2} 鈥� 鈭� 鈥� 16} 梅 \frac{s^{3} 鈥� + 鈥� 4 s^{2} 鈥� + 鈥� 16 s}{s^{3} 鈥� 鈭� 鈥� 64}$ .