Learning Objectives:

__Math Tutoring on Simplifying Rational Expressions__

First, let us define a **rational expression**. Let **u **and** v **be** polynomials,** then the expression, **u divided by v,** usually written in fraction form **u/v** is a **rational expression.** We should note that the domain of this **rational expression** is a set of all real numbers, for which the denominator does not equal zero. So, here are some examples of **rational expressions.** We can see two-thirds is a **rational expression.** So, we have dealt with these ways back in arithmetic, but now since the numerator and denominator can be polynomials, they can take on a variety of forms. For this **rational expression,** let us take a look at **simplifying rational expressions**. If we have a **rational expression **in the form of **u.w/v.w,** we can see there is a common factor of **w** between the numerator and denominator and we know that **w** divided by **w** would equal** 1**, so this **w **simplifies out and we are left with the simplified **rational expression u/v.** So, to **simplify** a** rational expression, **what we are going to do is, factor the numerator and denominator completely and then simplify out the common factors.

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**Hook Questions:**

*1. What is the rational expression?*

*2. What is the first step in simplifying a rational expression? *

*3. How do you multiply and divide rational expressions?*

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