Adding and Subtracting Rational Expressions

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Chapter 9

• Section 5
• Adding and Subtracting Rational Expressions

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Review Problems

• Find the least common multiple of the two
  numbers.
• 7, 21 24, 10 11,17

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Add or Subtract
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Add or Subtract
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How to find the LCM/LCD(Least Common
Multiple/Denominator)

1. Factor the denominator into its prime factors (as
   small as each will go).
2. Write each prime factor the greatest number of
   times it appears in either expression.
3. Simplify where possible.

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Find the Least Common Multiple

• 4x2 36 and 6x2 36x 54

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Find the Least Common Multiple

• 3x2 9x 30 and 6x 30

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Find the Least Common Multiple

• 5x2 15x 10 and 2x2 8

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Steps to Add/Subtract

1. Factor the denominators
2. Identify the LCD for multiplication
3. Multiply as needed
4. Add/subtract
5. Simplify

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Simplify
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Simplify
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Simplify
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Simplify
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Simplify
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Complex Fractions

• A fraction that has a fraction in its numerator
  or denominator or both
• Ex
• Two methods to simplify
• 1. Multiply everything by the LCD
• 2. Divide the numerator by the denominator

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Method 1 Multiplying by LCD

1. Find the LCD of the ENTIRE fraction
2. Multiply everything by this LCD (notice that the
   small fractions disappear)
3. Simplify

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2. Dividing

1. Simplify the numerator and denominator
2. Divide the numerator by the denominator

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