Rational Expressions

By Sarah Durr

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

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Want a short cut for multiplying and dividing rational expressions?

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

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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