Q 122. Divide Rational Expressions: 聽4... [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 122. (page 931)

Divide Rational Expressions: $\frac{4 n^{2} 鈥� + 鈥� 32 n}{3 n 鈥� + 鈥� 2} 脳 \frac{3 n^{2} 鈥� 鈭� 鈥� n 鈥� 鈭� 鈥� 2}{n^{2} 鈥� + 鈥� n 鈥� 鈭� 鈥� 30} 鈥� 鈥� 梅 \frac{108 n^{2} 鈥� 鈭� 鈥� 24 n}{n 鈥� + 鈥� 6}$

Short Answer

Expert verified

The required answer is $\frac{(n + 8) (n - 1)}{3 (n - 5) (9 n - 2)}$ .

Step by step solution

Step 1. Given information.

The given expression is $\frac{4 n^{2} 鈥� + 鈥� 32 n}{3 n 鈥� + 鈥� 2} 脳 \frac{3 n^{2} 鈥� 鈭� 鈥� n 鈥� 鈭� 鈥� 2}{n^{2} 鈥� + 鈥� n 鈥� 鈭� 鈥� 30} 鈥� 鈥� 梅 \frac{108 n^{2} 鈥� 鈭� 鈥� 24 n}{n 鈥� + 鈥� 6}$ .

Step 2. Simplify the expression.

$\frac{4 n^{2} 鈥� + 鈥� 32 n}{3 n 鈥� + 鈥� 2} 脳 \frac{3 n^{2} 鈥� 鈭� 鈥� n 鈥� 鈭� 鈥� 2}{n^{2} 鈥� + 鈥� n 鈥� 鈭� 鈥� 30} 鈥� 鈥� 梅 \frac{108 n^{2} 鈥� 鈭� 鈥� 24 n}{n 鈥� + 鈥� 6}$

Apply the fraction rule.

$\frac{\frac{4 n^{2} + 32 n}{3 n + 2} 脳 \frac{3 n^{2} - n - 2}{n^{2} + n - 30} (n + 6)}{108 n^{2} - 24 n} = \frac{\frac{(4 n^{2} + 32 n) (3 n + 2) (n - 1) (n + 6)}{(3 n + 2) (n^{2} + n - 30)}}{108 n^{2} - 24 n} = \frac{\frac{(4 n^{2} + 32 n) (3 n + 2) (n - 1) (n + 6)}{(3 n + 2) (n - 5) (n + 6)}}{108 n^{2} - 24 n} = \frac{(4 n^{2} + 32 n) (n - 1)}{(n - 5) (108 n^{2} - 24 n)}$

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

$\frac{(4 n^{2} + 32 n) (n - 1)}{(n - 5) (108 n^{2} - 24 n)} = \frac{4 n (n + 8) (n - 1)}{(n - 5) 路鈥� 12 n (9 n - 2)} = \frac{4 (n + 8) (n - 1)}{(n - 5) 路鈥� 4 路鈥� 3 (9 n - 2)} = \frac{(n + 8) (n - 1)}{3 (n - 5) (9 n - 2)}$

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91影视

Divide Rational Expressions: $\frac{4 n^{2} 鈥� + 鈥� 32 n}{3 n 鈥� + 鈥� 2} 脳 \frac{3 n^{2} 鈥� 鈭� 鈥� n 鈥� 鈭� 鈥� 2}{n^{2} 鈥� + 鈥� n 鈥� 鈭� 鈥� 30} 鈥� 鈥� 梅 \frac{108 n^{2} 鈥� 鈭� 鈥� 24 n}{n 鈥� + 鈥� 6}$

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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91影视

Divide Rational Expressions: 4n2鈥�+鈥�32n3n鈥�+鈥�2脳3n2鈥�鈭�鈥�n鈥�鈭�鈥�2n2鈥�+鈥�n鈥�鈭�鈥�30鈥�鈥�梅108n2鈥�鈭�鈥�24nn鈥�+鈥�6

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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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Applied Mathematics

Probability and Statistics

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Divide Rational Expressions: $\frac{4 n^{2} 鈥� + 鈥� 32 n}{3 n 鈥� + 鈥� 2} 脳 \frac{3 n^{2} 鈥� 鈭� 鈥� n 鈥� 鈭� 鈥� 2}{n^{2} 鈥� + 鈥� n 鈥� 鈭� 鈥� 30} 鈥� 鈥� 梅 \frac{108 n^{2} 鈥� 鈭� 鈥� 24 n}{n 鈥� + 鈥� 6}$