Solve each rational inequality by hand. Do not use a calculator. ((x+1)(x-2))/((x+3))<0

Name: Problem 61, Chapter 4: A Graphical Approach to College Algebra
Uploaded: 2020-07-20T12:00:17-08:00
Duration: 2 min 5 s
Channel: Ankit Gupta
Description: Solve each rational inequality by hand. Do not use a calculator. ((x+1)(x-2))/((x+3))<0

step 1 We have given x plus 1 multiplied with x minus 2 divided with x plus 3. Now this is less 0. Now

Solve each rational inequality by hand. Do not use a...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Rational Inequality

A rational inequality involves a ratio of polynomial expressions compared to zero or another value. Solving such an inequality requires understanding the behavior of the function across different intervals, as the sign (positive or negative) of the expression changes at its zeros and undefined points.

Critical Points

Critical points are the values where the numerator or denominator equals zero. These points, which include the zeros of the numerator (where the entire expression equals zero) and the zeros of the denominator (where the expression is undefined), divide the real number line into distinct intervals for further analysis.

Domain Restrictions

Domain restrictions arise from values that cause the denominator of the rational expression to be zero, making the expression undefined. It is essential to exclude these values from the solution set when solving the inequality.

Sign Chart Method

The sign chart method is a systematic technique used to determine the sign of a rational expression across different intervals. By testing points in each interval defined by the critical points, one can determine where the expression is positive or negative, ultimately identifying the intervals that satisfy the inequality.

Transcript

Please give Ace some feedback