### TEXT: Intermediate Algebra by Miller, OβNeill & Hyde

### Videos from Khan Academy.

A **rational expression** is a ratio of polynomials (p/q) with nonzero denominator (qβ 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 doΒ 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 nextΒ 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:

I figure out how to this from mathzone

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.

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.

I actually had fun in class its becoming more interesting

Pro. Halleck

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