Solving Rational Inequalities Analytically

Exercise 2.

Find the solutions of the inequality

\begin{displaymath}\frac{x+2}{x-1}\geq 1.\end{displaymath}


Rewrite as

\begin{displaymath}\frac{x+2}{x-1}-1\geq 0\end{displaymath}

and simplify the left side:

\begin{displaymath}\frac{x+2}{x-1}-1=\frac{(x+2)-(x-1)}{x-1}=\frac{3}{x-1}\geq 0.\end{displaymath}

This inequality has only one critical point, namely x=1.

The set of solutions of the inequality is the set $(1,\infty)$. x=1 is not a solution since it makes the denominator zero.

[Back] [Exercises]
[Algebra] [Trigonometry] [Complex Variables]
[Calculus] [Differential Equations] [Matrix Algebra]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Helmut Knaust

Copyright 1999-2019 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour