4.1-2 Rational Expressions

4.1-2 Rational Expressions - matching factors in any of the...

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4.1: Properties of Rational Expressions A rational expression is a ratio of polynomials with the denominator not equal to zero . The domain is the set of all real numbers that can replace the variables; that is, all real numbers except those that would cause the denominator to equal zero . Reducing a rational expression to lowest terms means to divide out any factors that are common to both the numerator and denominator; thus, both must be factored in order to find matching factors. State the domain of each rational expression: 1. x x 5 + 2. 2y -1 y 2 - 9 3. 3b + 1 2b 7b 4 2 - - 4. x x x x 2 5 3 4 2 2 - - - Reduce to lowest terms: 5. 242 154 6. 6a 3 b 12 c 5 8ab 4 c 9 - 7. 2x 2 + + - 10 12 2 8 2 x x 8. 3 3 x x - -
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4.2 Multiplication and Division To multiply rational expressions, first divide out any factors in any of the numerators that have
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Unformatted text preview: matching factors in any of the denominators; then multiply any remaining factors in the numerators and then any remaining factors in the denominators. Division is the same, except that we multiply by the reciprocal of the divisor. Perform the indicated operations. Write answers in lowest terms. 1. 3 7 14 9 2 x y y x ⋅ 2. 3 3 3 3 9 6 18 2 a y a y ab by b b---+ ⋅-+ 3. 19 12 1 1 12 3 2 x y y x-⋅-4. 60 48 9 2 4 3 x y z x y ÷ ( ) 5. 3 5 2 3 4 2 6 4 24 6 16 8 4 48 3 16 2 x x x x x x x x x + + + ÷--6. x x x x x x 2 2 2 5 6 3 6 9 4 + + ÷ + ⋅-7. b xb b xb x b xb b xb b xb x b xb 6 2 3 16 8 8 4 9 3 3 24 12 8 4 2 2 2 2--+ +--÷ + + +-+-8. ( 29 1 1 1 1 1 2 3 3 2 + + ⋅--÷ +-k k k k k k...
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This note was uploaded on 01/04/2012 for the course MATH 1033 taught by Professor Patriciabishop during the Fall '11 term at Miami Dade College, Miami.

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4.1-2 Rational Expressions - matching factors in any of the...

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