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7.5 – Adding and Subtracting Rational Expressions
Key Terms
 Common Denominator – A common multiple of the denominators of two or more fractions.
 Least Common Denominator (LCM) – The smallest common multiple of the denominators of two or more fractions.
Review
Fractions with the Same Denominator 
 To add or subtract fractions or rational expressions that have the same denominator.
 Add or subtract the numerators.
 Keep the common denominator.

Fractions with Different Denominators 

Notes
Finding the Common Denominator 
 You can find a common denominator of two rational expressions by multiplying the two denominators together.

 Another way to find the common denominator of two fractions is to find the least common denominator, which is the least common multiple (LCM) of the two denominators.
 How to Use the LCM to Add or Subtract Fractions
 Find the LCM of the two denominators.
 Rewrite both fractions using this LCM for both denominators.
 Add or subtract those fractions.

 LCM – You can also use the least common multiple as a common denominator to add or subtract rational expressions.
 Factor the denominator of each rational expression.
 Find the LCM of the denominators.
 Multiply the numerator and denominator of each rational expression by the factor(s) that make the denominator the LCM.
 Then you can add or subtract.
 Expressions
 Factor each denominator first!
 Then, ask yourself, “What am I missing from each denominator to make them look the same?”

Denominators with Variables (Exceptions) 
 When you have rational expressions as denominators, you need to determine what value(s) x cannot equal.
 Remember, denominators cannot equal 0 (undefined).
 Ex. For , x ≠ 0 and x ≠ 2.
 To find this, set each factor of the denominator not equal to zero
 and and solve.

Examples
Rational Expressions with Unlike Denominators 

RealWorld 
 Ex 2a. It takes you 45 minutes to wash a car alone. Your friend can wash a car in 30 minutes. How long will it take you and your friend to wash a car together?
 You –> 1 car every 45 min. Friend –> 1 car every 30 min.
 You: + Friend: = Together


 This reduces by , so divide by this to get
 Answer: Together, you can wash 1 car every 18 minutes.

 Ex 2b. How many cars per hour is this? Convert using
 So, that’s about 3 and 1/3 cars per hour.

Important!
Practice (Apex Study 7.5)
 Try practice problems on Pg 14
 Mandatory: write and answer problems on Pg 15
 1 Quiz
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