Q 124. Divide Rational Expressions:聽12... [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 124. (page 931)

Divide Rational Expressions: $\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$

Short Answer

Expert verified

The required answer is $\frac{(4 p + 1) (p - 4)}{3 p (p + 9) (p - 1)}$ .

Step by step solution

Step 1. Given information.

The given expression is $\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$ .

Step 2. Simplify the expression.

$\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}} = (\frac{\frac{12 p^{2} + 3 p}{p + 3}}{\frac{p^{2} + 2 p - 63}{p^{2} - p - 12}}) \frac{p - 7}{9 p^{3} - 9 p^{2}}$

Apply the fraction rule.

$= \frac{(12 p^{2} + 3 p) (p^{2} - p - 12)}{(p + 3) (p^{2} + 2 p - 63)} 脳 \frac{p - 7}{9 p^{3} - 9 p^{2}} = \frac{(12 p^{2} + 3 p) (p - 4) (p + 3)}{(p + 3) (p^{2} + 2 p - 63)} 脳 \frac{p - 7}{9 p^{3} - 9 p^{2}} = \frac{(12 p^{2} + 3 p) (p - 4) (p - 7)}{(p^{2} + 2 p - 63) (9 p^{3} - 9 p^{2})} = \frac{(12 p^{2} + 3 p) (p - 4) (p - 7)}{(p - 7) (p + 9) (9 p^{3} - 9 p^{2})} = \frac{(12 p^{2} + 3 p) (p - 4)}{(p + 9) (9 p^{3} - 9 p^{2})}$

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

$\frac{3 p (4 p + 1) (p - 4)}{(p + 9) (9 p^{3} - 9 p^{2})} = \frac{3 p (4 p + 1) (p - 4)}{(p + 9) 脳鈥� 9 p^{2} (p - 1)} = \frac{3 p (4 p + 1) (p - 4)}{(p + 9) 脳鈥� 3 脳鈥� 3 p^{2} (p - 1)} = \frac{p (4 p + 1) (p - 4)}{(p + 9) 脳鈥� 3 p^{2} (p - 1)} = \frac{p (4 p + 1) (p - 4)}{(p + 9) 脳鈥� 3 p p (p - 1)} = \frac{(4 p + 1) (p - 4)}{3 p (p + 9) (p - 1)}$

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Divide Rational Expressions: $\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$

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:12p2鈥�+鈥�3pp鈥�+鈥�3梅p2+鈥�2p鈥�鈭�鈥�63p2鈥�鈭�鈥�p鈥�鈭�鈥�12鈥�鈥�脳p鈥�鈭�鈥�79p3鈥�鈭�鈥�9p2

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

Probability and Statistics

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Divide Rational Expressions: $\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$