Lesson 3

Lesson 3 Summary

Photodisc/Thinkstock

In this lesson you investigated the following questions:

• How are adding and subtracting rational expressions similar to adding and subtracting rational numbers?
  
  
• What patterns can be used to prepare rational expressions for addition or subtraction?

You discovered that adding and subtracting rational expressions is similar to adding and subtracting rational numbers. In both cases, you must do the following:

Step 1: Determine the lowest common denominator (LCD).

Step 2: Use the property of 1 to write equivalent rational expressions over the LCD.

Step 3: Add or subtract the numerators, and then simplify.

You discovered that the steps in the procedure cannot be applied out of order if the correct answer is desired. You learned two strategies for determining the lowest common denominator. One method is based on a strategy similar to prime factorization. The other method is based on the pattern that the lowest common denominator is equal to the product of the denominators divided by the greatest common factor:

In the next lesson you will learn how to solve rational equations. You will continue to see how useful the lowest common denominator is in solving these types of equations.