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Transcript
Int. Alg. Notes Section 6.1 Page 1 of 4 Section 6.1: Multiplying and Dividing Rational Expressions Big Idea: A rational expression is the quotient of two polynomials. We study them because they incorporate the arithmetic operation of division (polynomials only used addition, subtraction, and multiplication). We multiply and divide rational expressions in the same way we multiply or divide arithmetic fractions… Big Skill: You should be able to identify the domain of a rational expression, simplify a rational expression by cancelling common factors, and multiply and divide rational expressions using the familiar rules from arithmetic. Examples of rational expressions: x5 1 x 2 7 x 18 2 2x 1 x3 x 4 The domain of a rational expression is the set of all numbers which can be plugged into the rational expression. To find the domain of a rational expression, find all values of the variable that cause the denominator to be zero, and exclude them from the domain. Practice: find the domain of the above rational expressions. A rational expression is simplified when all common factors in the numerator and denominator have been cancelled. Examples: 12 2 2 3 2 2 3 3 20 2 2 5 2 2 5 5 x 5 x 3 x 5 x 2 2 x 15 x 5 x 3 2 2 x 3x 9 2 x 3 x 3 2 x 3 x 3 2 x 3 Practice: 1. Simplify x2 x 6 2 x2 5x 2 Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Int. Alg. Notes 2. Simplify y 3 27 2 y2 6 y 3. Simplify 10 2 x 4 x 2 20 x 4. Simplify 3w2 13w 10 2 3w Section 6.1 Page 2 of 4 a c ac b d bd a c a d ad To divide rational expressions, use the arithmetic rule (i.e., invert and multiply) b d b c bc To multiply rational expressions, use the arithmetic rule Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Int. Alg. Notes Section 6.1 Page 3 of 4 Practice: 1. Simplify n2 9 n2 2 n 5n 6 6 2n 2. Simplify a 2 b2 10a 5b 2 2 10a 10ab 2a 3ab b2 45 z 4 7y 3. Simplify 5z 21y 2 Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Int. Alg. Notes Section 6.1 Page 4 of 4 p3 8 5 p 2 15 p 4. Simplify p2 4 p2 3 p m 2 5m m7 5. Simplify 2m m 2 6m 7 A rational function is a function of the form p x R x q x Where p and q are polynomial functions and q is not the zero of the polynomial. The domain consists of all real numbers except those for which the denominator q is zero. Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.