Skip Navigation Links
Rational Expression
To enroll in any of our courses, click here
Rational Expression
A rational expression is an algebraic expression of the form R/S, where R and S are simple expressions (usually polynomials), and the denominator S is not zero.

To write a rational expression in lowest terms, first find all common factors (constants, variables, or polynomials) of the numerator and the denominator. So, factor the numerator and the denominator. Then cross out all common factors.
People who saw this lesson also found the
following lessons useful:
Arithmetic Progression
Circle: Chord
Circle: Tangent
System of Simultaneous Linear Equations
Similar Traingles(Angles are Congruent)
Example: Reduce the following rational expressions to its lowest terms.
(i) x2+10x+24/x2+5x-6      
(ii) x2+7x+12/x2+5x+6


(i)Given: x2+10x+24/x2+5x-6   
Let p(x) = x2+10x+24 = (x+6)(x+4)
And q(x) = x2+5x-6 = (x+6)(x-1)
So, g.c.d.[p(x),q(x)]= x+6.

= (x+6)(x+4)/(x+6)(x-1)
= (x+4)/(x-1) .....[Cancelling the g.c.d.]

Hence, the given rational expression in lowest terms is (x+4)/(x-1).

(ii)Given: x2+7x+12/x2+5x+6
Let p(x) = x2+7x+12 = (x+3)(x+4)
And q(x) = x2+5x+6 = (x+3)(x+2)
So, g.c.d.[p(x),q(x)]= x+3.

= (x+3)(x+4)/(x+3)(x+2)
= (x+4)/(x+2).....[Cancelling the g.c.d.]

Hence, the given rational expression in lowest terms is (x+4)/(x+2).
As many of you know, Winpossible's online courses use a unique teaching method where an instructor explains the concepts in any given area to you in his/her own voice and handwriting, just like you see your teacher explain things to you on a blackboard in your classroom. All our courses include teacher's instruction, practice questions as well as end-of-lesson quizzes for practice. You can enroll in any of our online courses by clicking here.

The format of Winpossible's online courses is also very suitable for teachers who are using an interactive whiteboard such as Smartboard on Promethean in their classrooms, because the course lessons can be easily displayed on such interactive whiteboards. Volume pricing is available for schools interested in our online courses. For more information, please contact us at

 Copyright © Winpossible, 2010 - 2011
Best viewed in 1024x768 & IE 5.0 or later version