Chapter 5: Q 2. (page 297)

Solve the inequality : $\frac{x - 1}{x + 4} > 0$

Short Answer

Expert verified

Domain of the function should be $\frac{x - 1}{x + 4} > 0$ , therefore $(x - 1)$ and $(x + 4)$ must remain either positive or negative simultaneously.

For, $(x - 1) > 0$ , the value of $x$ should be $(1, \infty)$ and $(x + 4) > 0$ , the value of $x$ should be $(- 4, \infty)$

Again, $(x - 1) < 0$ , the value of $x$ should be $(- \infty, 1)$ and $(x + 4) < 0$ , the value will be $(- \infty, - 4)$

Hence, the solution is $x \in (- \infty, - 4) \cup (- 4, + \infty)$

Step by step solution

Step 1. Given information

Given expression is $\frac{x - 1}{x + 4} > 0$

Step 2. Calculation

Solving the inequalities, the function consists all real number excepts $(- 4)$ , the domain will be $(- \infty, - 4) \cup (- 4, + \infty)$ .

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.

Solve the inequality : $\frac{x - 1}{x + 4} > 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Probability and Statistics

Geometry

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve the inequality :x-1x+4>0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Probability and Statistics

Geometry

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve the inequality : $\frac{x - 1}{x + 4} > 0$