Learning Objectives
Introduction
Tutorial
Adding or Subtracting Rational Expressions
with Common Denominators
Step 2: Put the sum or difference found in step 1 over the common denominator.
Step 3: Reduce to lowest
terms as shown in Tutorial 8: Simplifying
Rational Expressions.
Why do we have to have a common denominator
when
we add or subtract rational expressions?????
Example 1: Add .
AND
Step 2: Put the sum or
difference found in step 1 over the common denominator.
*Combine the numerators
*Write over common denominator
*Excluded values of the original den.
Also note that the value that would be excluded from the domain is
2/5. This is the value that makes the original denominator
equal to 0.
Example 2: Subtract .
AND
Step 2: Put the sum or
difference found in step 1 over the common denominator.
*Combine the numerators
*Write over common denominator
*Factor the num.
*Simplify by div. out the common factor of (y - 1)
*Excluded values of the original den.
Least Common Denominator (LCD)
Step 2: The LCD is the list of all the DIFFERENT factors in the denominators raised to the highest power that there is of each factor.
Now the question is WHAT do we multiply top and bottom by to get what we want? We need to have the LCD, so you look to see what factor(s) are missing from the original denominator that is in the LCD. If there are any missing factors then that is what you need to multiply the numerator AND denominator by.
Example 3: Add .
*Rewriting denominator in factored form
*Mult. top and bottom by (y - 4)
*Combine the numerators
*Write over common denominator
*Simplify by div. out the common factor of y
*Excluded values of the original den.
Example 4: Add .
*Missing the factor of (x +
1) in the den.
*Mult. top and bottom by (x +
1)
*Excluded values of the original den.
Example 5: Subtract .
*Missing the factor of (x -
8) in the den.
*Mult. top and bottom by (x -
8)
*Missing the factor of (x +
5) in the den.
*Mult. top and bottom by (x +
5)
*Distribute the minus sign through the (
)
*No common factors to divide out
*Excluded values of the original den.
Practice Problems
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1b: Perform the indicated operation.
Need Extra Help on these Topics?
http://www.purplemath.com/modules/rtnladd.htm
This webpage goes over finding the least common denominator and combining
rational expressions.
Go to Get Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for some
more suggestions.
Videos at this site were created and produced by Kim Seward and Virginia Williams Trice.
Last revised on Dec. 15, 2009 by Kim Seward.
All contents copyright (C) 2002 - 2010, WTAMU and Kim Seward. All rights reserved.