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Published byBenedict Sullivan Modified over 8 years ago
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Rational Expressions 6.1
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The expression is one term (monomial). It has four factors. Factors are things that are multiplied. How many factors? six
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How many terms? TWO How many factors? TWO How many terms? TWO How many factors? TWO or, FOUR Monomials can be factored into “pieces”.
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SIMPLIFYING RATIONAL EXPRESSIONS
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3 4 3 2 1 1 2 7 1 1 In elementary school, we learned to cancel fractions for “one.” This technique is also used in “reducing” fractions.
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We have rational expressions That must be simplified. One main rule we have to follow: Cancel what is multiplied. We need factors. We must factor. GCF is first! Difference of two squares, grouping, Also FOIL reversed. Tune: I’ve been workin’ on the railroad.
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We have rational expressions that must be simplified. One main rule we have to follow: cancel what is multiplied. NO!! We need factors. We must factor.
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Difference of two squares GCF is first Doesn’t need factoring FOIL Reversed
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GCF is first Doesn’t need factoring FOIL Reversed Difference of two squares
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There is only one monomial, so it cannot be cancelled: We are dividing out fractions for “one.”
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Steps for simplifying: Put each polynomial in descending order Look for a GCF. If the first term is negative, factor out a negative. Then factor using FOIL, Grouping, DOTS, etc.
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Steps for simplifying: Then cancel. You can cancel pieces of monomials with similar pieces of other monomials, but binomials can only be cancelled if they are exactly alike.
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Example: Put each polynomial in descending order Factor out the GCF first: Continue factoring:
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First cancel pieces of monomials: Then cancel exact binomials: Write answer as one fraction:
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