# Rational Expressions

## What is a rational expression?

A fraction in which the numerator and/or the denominator are polynomials.

## Simplifying Rational Expressions

Before you can multiply, divide, add, or subtract rational expressions, you first must simplify the expression. To do this, you must follow these three steps:

1. factor both the numerator and denominator

2. eliminate common factors

3. simplify

4. check to see under which conditions is the expression undefined

## 4. Check for undefined

Find the values that would make the denominator equal to 0. The denominator in this expression is y(y+2)(y-3). These values are 0, -2, and 3, so when y=0, -2, or 3 the expression is undefined.

## Multiplying & Dividing Rational Expressions

Multiplying and dividing rational expressions are essentially the same thing except dividing rational expressions involves one extra step at the beginning: switching the numerator and denominator of ONE of the expressions. Then you follow the multiplication steps, as stated below:

1. (if division) switch the numerator and denominator of one of the expressions (A.K.A. changing it to a multiplication expression)

2. write out the factors for EVERYTHING

3. eliminate all common factors

4. simplify expression  ## Simplifying Rational Expressions Before Multiplying & Dividing

You can use your skills from simplifying rational expressions to make multiplying and dividing a lot simpler! Just follow these steps:

1. (if division) switch the numerator and denominator of one of the expressions (A.K.A. changing it to a multiplication expression)

2. factor the polynomials

3. eliminate common factors

4. simplify

5. multiply ## Summary of Topics in Today's Newsletter

1. Simplifying Rational Expressions

2. Multiplying & Dividing Rational Expressions

3. Simplifying Rational Expressions Before Multiplying & Dividing (A.K.A. Making Polynomials in the Numerator and Denominator)

## Mark Your Calendar!!

Quiz 4: Tuesday, 12.8.2015

Test 2: Thursday, 12.10.2015