## Tutoring on Simplifying Rational Expressions

Learning Objectives:

#### Understand to Simplify Rational Expressions

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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