# Day 17 – Rational Expressions: Simplify, Multiply, Divide

### TEXT: Intermediate Algebra by Miller, O’Neill & Hyde

A rational expression is a ratio of polynomials (p/q) with nonzero denominator (q≠0).

A rational expression can be simplified using the following principle: It is a good idea to always put a property or procedure into your own words. Do that now before proceeding.

Here is the first video:

The next 2 videos do  more complicated situations and also find the domain. Rational expressions can be thought of as functions. The domain of a function is where it is defined (technically the set of inputs). To find the domain of a rational function, you find where the denominator is 0 and then exclude those points.

Multiplication of rational expressions relies on: The first video does an example where the polynomials in our rational expressions are monomials:

The next  video gives a more complicated example:

To divide, we use the following principle to transform the quotient into a multiplication of rational expressions (and then use the multiplication property): Put the property (or procedure) into your own words before proceeding.

Here is a video presenting an example:

### 5 Responses to Day 17 – Rational Expressions: Simplify, Multiply, Divide

1. brina92 says:

I figure out how to this from mathzone

2. Hibba says:

I am little confused about this lesson, I did not get to we can state the domain.
I need more help with stating the domain.

3. Ezra Halleck says:

The tricky thing is the logic. By setting the denominator to 0 and solving for the variable, you are not finding the domain. You are finding what is known as the complement of the domain. Visually, the domain for a rational function is going to be the entire real number line with some holes in it. Those holes are precisely where the denominator is 0.

4. sbailey says:

I actually had fun in class its becoming more interesting

5. awiltshire says:

Pro. Halleck

Okay so I get it, but would have like to do more division examples