RATL 2 | Lesson 1 | Explore 2 (Simplifying Rational Expressions)

Simplifying Rational Expressions

Simplifying a rational expression is done much the same way as simplifying a fraction.

Example 1: The monomials in the numerator and denominator below can be expanded through complete factorization. Then, all of the ones in the form of a number or variable over itself can be divided out. Examples of representations of one include \(\dfrac{3}{3}\) and \(\dfrac{x}{x}\).


Example 2: This example has polynomials  in the numerator and denominator.

First factor, if possible.


As with the monomials in the first example, simplify by dividing out any forms of one, whether they are monomials or polynomials. In this case, \(\dfrac{x+4}{x+4}\) is a form of 1.

The simplified form of this rational expression is:


Remember only factors can be divided out, not terms by themselves! \(\dfrac{x+4}{x+6}\) The “x’s” cannot be divided out of this expression!

Example 3: This rational expression has polynomials in the numerator and denominator that can be factored.  There are multiple forms of one that can be divided out to reveal a much simpler form of the expression.


Practice (Simplifying Rational Expressions)