9.5

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9.5 Adding and Subtracting Rational Expressions
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In order to add or subtract fractions we need a
common denominator
LCD 15
LCD 36
We want the Lowest Common Denominator (LCD)
before we add or subtract
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ADDING and SUBTRACTINGRATIONALS - Finding LCM
70x²

• 10x², 35x² ? _______________________
• 4x³ , 5x²y ? _______________________
• x-y , x²-y² ? _______________________
• x²-5x4 , x 2 ? ___________________

20x³y
(x-y)(xy)
(x-4)(x-1)(x-2)
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ADDING and SUBTRACTINGAdding

• ADD/SUBTRACT Rules
• Factor denominators
• Find LCM
• Multiply each term to get denominator LCM
• /- and combine like terms
• Simplify more if possible

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ADDING and SUBTRACTINGSubtracting
Factor denominators
Multiply terms to get LCMs on bottom
Simplify
Simplify
Combine like terms
Factor top
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ADDING and SUBTRACTING A Toughie
FACTOR
FACTOR -OUT
CONVERT
SIMPLIFY
COMBINE
SIMPLIFY
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Lets try one
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Lets try one
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Lets try one
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COMPLEX FRACTIONS

• What are complex fractions?

Complex fractions are giant expressions where
there are fractions within fractions.
The goal is to simplify them down to normal
fractions.
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EX simplify

• SIMPLIFYING COMPLEX FRACTIONS STEPS
• Find LCM of denoms
• Treat each fraction as an individual problem.
  Find the LCM and add or subtract.
• Divide the rational expressions.
• Simplify

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EX - simplify
DIVIDE THE RATIONALS
DISTRIBUTE LCM
FACTOR OUT -1
SIMPLIFY
MULT TOP/BOT by LCM
SIMPLIFY
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