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 $\frac{x - 3}{x + 9}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Statistics

Calculus

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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

Geometry

Probability and Statistics

Statistics

Calculus

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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