Q.487. Perform the indicated operation ... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q.487. (page 742)

Perform the indicated operation and simplify.
$\frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81}$

Short Answer

Expert verified

The solution is $\frac{x - 3}{x + 9}$ .

Step by step solution

Step 1. Given information.

The given expression is $\frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81}$ .

Step 2. Simplify the expression.

$\frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81} = \frac{6 x^{2} - x + 20 - 5 x^{2} - 11 x + 7}{x^{2} - 81} \frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81} = \frac{6 x^{2} - 5 x^{2} - x - 11 x + 20 + 7}{x^{2} - 81} \frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81} = \frac{x^{2} - 12 x + 27}{x^{2} - 81} \frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81} = \frac{x^{2} - 9 x - 3 x + 27}{x^{2} - 81} \frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81} = \frac{x (x - 9) - 3 (x - 9)}{(x - 9) (x + 9)} \frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81} = \frac{(x - 9) (x - 3)}{(x - 9) (x + 9)} (R e m o v e t h e c o m m o n f a c t o r) \frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81} = \frac{x - 3}{x + 9}$

Step 3. Simplified answer.

Hence, the simplified expression is $\frac{x - 3}{x + 9}$ .

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91影视

Perform the indicated operation and simplify.
$\frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Simplified answer.

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91影视

Perform the indicated operation and simplify.6x2-x+20x2-81-5x2+11x-7x2-81

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Perform the indicated operation and simplify.
$\frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81}$