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Adding and Subtracting Rational Expression - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Adding and subtracting rational expressions is similar to adding fractions. When adding and subtracting rational expressions, we find a common denominator and then add the numerators. To find a common denominator, factor each first. This strategy is especially important when the denominators are trinomials.

Recall and rational expression is a fraction that polynomials in top and bottom. So when you're working with rational expressions that means you're working with ugly fractions. That means for some of you guys this is going to be a really difficult chapter in your Math class if you don't have a strong fraction background. Think back to your third and fourth grade teachers. If those people weren't very good teachers you're in big trouble. But don't worry I'm going to help you with them, so the first thing I want you guys to think about when you're adding and subtracting fractions, go back to your third and fourth grade classes and how you had to do common denominators.
You're going to have to do common denominators for this rational fractions with x's and polynomials and stuff. So before you start your homework it's a good idea to review what you already know. Check it out if I had to add these 3 things when I think back to my third grade teacher Mrs. Manning she taught me that I had to find the common denominator for each one of these. 9 fourths, one half and negative 3, I'm going to write that as negative 3 over 1 so that I can see that as a fraction. These denominators all need to be the same so I'm thinking about, what number do 4, 2 and 1 all multiply into. And the number they multiply into is 4, in order for that to be a 4 it has to get multiplied by 2 over 2 I'm really just multiplying by 1 there right? 2 over 2 is equal to the value of 1, I haven't changed the value of that one half. Same thing here, if I want that to be a 4 in the denominator I'm going to have multiply that guy by 4 over 4.
Now let's rewrite it 9 fourths plus 2 fourths take away 12 fourths now I can combine these fractions because they have common denominators. That's the most important step you guys are going to have to remember when adding or subtracting rational functions. They have to have the exact same denominator in order for them to be combined, then you just look at the tops 9 plus 2 is 11, 11 take away 12 is negative 1. So my final answer for that sum and difference is going to be negative one fourth. Keep those ideas of finding common denominators in mind when you guys move into your homework about adding and subtracting rational expressions.

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