Oct. 1 Class

Learning Goals: Understand how to add and subtract rational expressions.

We began with a review of how to add fractions, something you should all know from grade 9!

For example, look this:

Easy?  Let's break down all the steps we used to get to the final answer.

1. Find the lowest common denominator.
2. Rewrite the numerators.
3. Add the numerators.

Now we need to apply this to rational expressions.

Example: Add the following, .

The lowest common denominator in this case is 3y.

We rewire the numerators as,.

Now we add the numerators,

And we're done.

Example: Add the following, .

We treat the denominators as factors.  In this case the lowest common denominator is,

LCD: (x+2)(x–3)

Rewrite the numerators, .

Add the numerators, 

And you get the solution: . Restrictions: x ≠ 2, x ≠ 3.

A few things to remember:

• You should always try to simplify.
• Don't simplify until the end when everything is in factored form.
• You cannot simplify when there is still adding and subtracting to be done.