Rational Expressions

The definition of rational expressions and their domains are examined.

Definition

A rational expression is the quotient of two polynomials.

Examples of Rational Expressions


rational expressions 1

Domain of Rational Expressions

It is clear that the above expressions are undefined if a division by 0 occurs. The domain of a rational expression excludes all values that make the denominator equal to 0.
  1. The domain of the rational expression (x - 1) / (x + 2)

    is the set of all real numbers except x = - 2

  2. The domain of the rational expression (x + 1) / ((x + 2)(x - 3))

    is the set of all real numbers except x = -2 and x = 3

  3. The domain of the rational expression 1 / (x2 + 1)

    is the set of all real numbers since the denominator x2 + 1 cannot be 0 for any real number x.

  4. To find the domain of the rational expression, (x2 + 4) / (x3 + 2 x2 - 3 x)

    we first have to factor the denominator and find its zeros.

    x3 + 2 x2 - 3 x = x(x2 + 2 x - 3)

    = x(x - 1)(x + 3)

    The domain of the above rational expressions is the set of all real numbers except x = 0, x = 1 and x = - 3.

Exercises

Find the domain of each of the Rational Expressions given below.

rational expressions 1

Answers to the above exercises



More references to topics related to rational expressions.


Home Page -- HTML5 Math Applets for Mobile Learning -- Math Formulas for Mobile Learning -- Algebra Questions -- Math Worksheets -- Free Compass Math tests Practice
Free Practice for SAT, ACT Math tests -- GRE practice -- GMAT practice Precalculus Tutorials -- Precalculus Questions and Problems -- Precalculus Applets -- Equations, Systems and Inequalities -- Online Calculators -- Graphing -- Trigonometry -- Trigonometry Worsheets -- Geometry Tutorials -- Geometry Calculators -- Geometry Worksheets -- Calculus Tutorials -- Calculus Questions -- Calculus Worksheets -- Applied Math -- Antennas -- Math Software -- Elementary Statistics High School Math -- Middle School Math -- Primary Math
Math Videos From Analyzemath
Author - e-mail


Updated: 2 April 2013

Copyright © 2003 - 2014 - All rights reserved