Multiplying and Dividing Rational Expressions

Last piece of material for this unit. Today we learned to multiply and divide rational expressions.

Ms. Talley's students, you have a test today or tomorrow. My 2A and 4A, we will do a quiz on Monday. It will cover:
(1) Simplifying Rational Expressions (see notes 2 blog posts back)
(2) Adding and Subtracting Rational Expressions (see notes in my last blog post), and
(3) Multiplying and Dividing Rational Expressions (see below for the notes)

Here are the notes:

First, multiplying and diving NUMBER fractions (this should be a review):

  Multiplying and Dividing Rational Expressions, with variables and factors, works the same way:

 

Adding and Subtracting Fractions and Rational Expressions

You can add or subtract fractions as long as they have the same (common) denominator:

 

If the denominators are different, you first have to find the LEAST COMMON DENOMINATOR.

That's the smallest number that BOTH denominators will go into evenly:

For example: 

Denominators 3, 4 ; Common denominator is 12 because 3 and 4 both go into 12.

Denominators 15 and 20 ; Common denominator is 60 because 15 and 20 both go into 60.

15*20 = 300, which would be a common denominator but not the smallest one. So you'd have to simplify a lot later.

15 = 3*5

20 = 2*2*5

So the LEAST COMMON DENOMINATOR is 3*5*2*2 = 60.

  

More examples:

 Rational Expressions work the same way. If you already have a common denominator, just add or subtract (whichever it says to do) the numerators, combine any like terms, and simplify if possible:

 If the denominators are not common, you need to find the least common denominator that includes all the factors of both denominators.

This is just like with number fractions!

Notes on Simplifying Rational Expressions (January 11, 2016), + Homework

Here are today's notes and examples:

And here is the homework assignment, due AT THE START OF CLASS WEDNESDAY:

Welcome back!

I'm so glad to see y'all in class again!

Here are the notes from today's Advanced Algebra class - the last problem on it is your homework, due tomorrow!

And, here are the notes from Advanced Algebra Support today, on going back and forth between ROOTS and FACTORS. I strongly suggest that you practice this until you are comfortable. It's very important.