Purpose: To simplify fractions'

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6.1 p. 247

• Purpose To simplify fractions.
• Homework P. 248 249 1-29 odd

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Example 1

• In order to simplify fractions, you must have
  like terms.
• 2t 6 It doesnt look like you can
• 5t 15 cancel, BUT FACTOR!
• 2(t 3) Now that you have like terms,
• 5(t 3) cancel the (t 3) AND
• You get 2/5 as your answer.

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Example 2

• 5p 5q Some want to cancel the 5s and
• 5p 5q variables BUT this is WRONG!!
• You CANNOT cancel out parts of an equation. , -
  signs are like glue.
• You must factor first.
• 5(p q) p q
• 5(p q) p q

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Example 3

• 3x² 5x 2
• 6 x - x² FACTOR FIRST!!!
• (3x -1)(x 2)
• (3 x)(2 x) Because order in addition
  does not matter, the x 2 and 2 x cancel each
  other out.
• Your answer is 3x -1 3s cant cancel!
• 3 - x

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Example 4

• (a 5)² Rewrite and Factor
• 25 - a²
• (a 5)(a 5) It appears that nothing
• (5 a)(5 a) will cancel.
• Remember that a 5 and 5 a are opposites. By
  Multiplying by -1, you can reverse this.
• -1(5 a)(a 5) You can now cancel 5 a.
• (5 a)(5 a) -(a 5)/(a 5)

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Restrictions

• Although you wont be tested on these, you should
  know what they mean.
• Lets say you have 1/x. X can be anything BUT
  (0) because that is NO SOLUTION!
• So the restriction is x ? 0.
• Lets say you have 1/(x 2).
• The restriction is 2 because it would make 0 for
  the denominator which is N.S. SO
• X ? 2
• Some problems may have more than 1 number as a
  restriction.