1. Fractions - a Quick Review
Section 6.1 Rational Expression & Functions: Definitions, Multiplying, Dividing
Fractions - a Quick Review
Definitions: Rational Functions, Expressions
Finding the Domains (and Exclusions) of Rational Functions
Simplifying Rational Functions
Simplifying by factoring out -1
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2. Fractions - Review Q: When can you add or subtract fractions?
A: Only when denominators are the same
Q: What do you do when denominators are not the same?
A: Use their LCD to create equivalent fractions.
Q: How do you multiply fractions?
A: Factor all tops and factor all bottoms, cancel matching factors, multiply tops and bottoms
Q: What do you do first when dividing fractions?
A: Turn division into multiplication : reciprocal the divisor.
Rational Expressions are Polynomial Fractions ! Same rules!
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3. Definitions
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4. Finding the Domain (and exclusions) of a Rational Function
Recall the domain of a function is the set of
all real numbers for which the function is defined.
What real values make this function undefined (divided by 0)?
Factor: x2 + 2x – 24 = (x – 4)(x + 6)
{x | x is Real, except for 4 or -6}
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5. Graphs of Rational Functions
t=-5/2 is an Asymptote
2t + 5 ≠ 0
2t ≠ -5
t ≠ -5/2
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6. Definitions
Horizontal Asymptote – A horizontal line that the graph of a function approaches as x values get very large or very small.
Vertical Asymptote – A vertical line that the graph of a function approaches as x values approach a fixed number
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7. More Properties of Fractions - Review
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8. Simplifying Rational Expressions (In general, the expressions are NOT equivalent)
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9. First Factor and Identify domain exclusions, Then Simplify
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10. Multiplying Fractions
(First find domain exclusions)
Factor expressions, then cancel like factors
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11. Example – Step by Step x≠0,3 Write down original problem1 1 x 4 1 1
Write down original problem
Combine with parentheses
Find any polynomials that need factoring
Rewrite (if any factoring was done)
Identify domain exclusions
Cancel out matching factors
Simplify the answer
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12. Board Practice – Rational Multiplication
Write original problem
Combine w/ parens
Factor polynomials
Rewrite (if any factoring)
Identify domain exclusions
Cancel matching factors
Simplify the answer
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13. Finding Powers of Rational Expressions
Factor and Simplify (if possible) before applying the power
If part of a larger expression, see if any terms cancel out
Multiply out the terms in the numerator, multiply out the terms in the denominator.
Leave in simplified factored form
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14. Dividing Fractions
Change Divide to Multiply by Reciprocal, follow multiply procedure
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15. Board Practice - Rational Division
Write original problem
Combine w/ parens
Factor polynomials
Rewrite (if any factoring)
Identify domain exclusions
Cancel matching factors
Simplify the answer
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16. Mixed Operations Multiplications & Division are done left to right
In effect, make each divisor into a reciprocal
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17. What Next?
Present Section 6.2 Add/Subtract Rational Expressions
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