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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