Lesson 3

Lesson 3 Summary

 

In this lesson you investigated the following questions:

• How are adding and subtracting rational expressions similar to adding and subtracting rational numbers?
  
• Can you use the patterns of adding and subtracting rational numbers to determine, in simplified form, the addition or subtraction of rational expressions?

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: State any non-permissible values.

 

Step 2: Determine the lowest common denominator (LCD).

 

Step 3: Use the property of 1 to write equivalent rational expressions over the LCD.

 

Step 4: Add or subtract the numerators, and then simplify.

 

You discovered that the order of steps for these procedures is important. 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 continue to see how useful the lowest common denominator is when solving rational equations.