Chapter 11 Notes Alg. 1CP
11.2 “Rational Expressions”p. 583-585
Rational number: a number that can be written as the ______of two ______Examples:
Rational expression: an ______whose numerator and denominator are ______
Examples:
Excluded Values: any values of a ______that result in a ______of ______
Read Ex. 1
√1A) B)
Simplified Rational Expression: has no ______of the numerator and denominator.
Read Ex. 3
√3)
Read Ex. 4
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√4A)
B)
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11-3“Multiplying Rational Expressions”p. 590-591
Use the same methods you use for multiplying fractions:
- Multiply the ______together.
- Multiply the ______together.
- Reduce by cancelling ______factors of the numerator and denominator.
- You may cancel common factors ______and/or ______you multiply.
Read Ex. 1
√1A) B)
Read Ex. 2
Step 1 ______both the numerator and denominator of each fraction fully.
Ex
Step 2 Multiply the factors together to form ______.
Ex
Step 3 ______factors that are in both the numerator and denominator.
Ex
√2A)
B)
Read Ex. 3
3)
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11-4 Dividing Rational Expressions p. 595-597
Step 1Write the ______of the second fraction (the divisor) and change the problem into a multiplication problem.
Ex:
Step 2______both the numerator and denominator of each fraction fully and multiply the factors together to form ______.
Ex:
Step 3______factorsthat are in both the numerator and
denominator.
Ex:
Read Ex. 1 & 2
√1A) B)
C) D)
2A) B)
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11-5A “Dividing Polynomials: Fractions”p. 601-602
To divide a polynomial by a ______or ______polynomial:
Method A:
oEx:
oEx:
√1A) B)
√2A) B)
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11-5B “Dividing Polynomials”p. 602-603
To divide a polynomial by a ______especially when the numerator is ______:
Method B:
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Ex. A:
Ex. B:
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√3A) B)
Sometimes you have to insert a ______termto hold the place of a “missing term”.(Read Ex. 4 – p. 603)
Ex.
√4A) B)
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11-6“Rational Expressions with Like Denominators” p. 608-610
Add or subtract rational expressions just like any fractions,even if the denominators are ______.
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√1A) B)
√2A) B)
Read Ex. 3 and see diagrams (p. 609)
√3A) P = B) P =
Read Ex. 4
√4A) B)
Read Ex. 4
Sometimes you must express a denominator as its additive ______to have like denominators.
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√5A) B)
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