Rational Expressions Part 2

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Rational Expressions Part 2

• Gary Greer

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Adding and Subtracting Fractions

• We already know how to add and subtract fractions
• multiply bottoms to get new denominator
• cross multiply to get new numerators

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Rational Expressions Work the Same Way

• To find the common denominator for two rational
  expressions, multiply the denominators
• for this one the common denominator is (x)(y) or
  xy

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Lets try a harder one

• multiply the bottoms and then cross multiply
• once you have a common denominator, you can add
  the tops
• then simplify, in this case we factor
• finally we have the simplified answer

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Complex Fractions

• Sometimes we have a complex fraction
• here we can multiply the top and bottom by a
  common denominator and then simplify

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And a complex fraction with variables

• The process is the same multiply the top and the
  bottom by a common denominator for the fractions
  involved

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So lets do some serious problems

• When we look at these, we need to decide which
  approach is easiest
• in this case, it is easiest to simply multiply
  one term by the denominator of the other

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So lets do some serious problems

• Alternately we could have multiplied the bottoms
  and cross multiplied as usual

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So lets do some serious problems

• The method works no matter how complex the
  problem
• Here we multiply the bottoms and then cross
  multiply

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So lets do some serious problems

• The method works no matter how complex the
  problem
• Here we multiply the bottoms and then cross
  multiply

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So lets do some serious problems
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Solving Rational Expressions

• You have already learned to solve simple ones
• In this case multiply by the common denominator

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Solving Rational Expressions
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Solving Rational Expressions
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A tough one
x cannot be 5 or -5
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Continued