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Published byEthan Benson Modified over 4 years ago

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Rational Expressions Section 0.5

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Rational Expressions and domain restrictions Rational number- ratio of two integers with the denominator not equal to zero. Rational expression- ratio or quotient of two polynomials with the denominator not equal to zero Examples:Rational number: Rational expression: where x = 6

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Domain- set of real numbers that your algebraic expression is defined. Think about domain as what values are OK to plug into your equation. For rational expressions our domain will not be defined for the values that make the denominator zero. What is the domain for: Answer: All Real numbers except x = -3

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Find the domain for each algebraic expression Domain: All real numbers Domain: All real numbers except x = 0 Domain: All real numbers except Domain: All real numbers

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Find the domain for each algebraic expression Domain: All real numbers except x = 0 and x = 5 Domain: All real numbers except x = 4 and x = -4

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Reduce the rational expression Where x = -1 Where x = -5

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Multiply the rational expressions and simplify Check domain at factored step: Domain: All reals except:

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Multiply Domain Restrictions: if!

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Divide the rational expressions Domain: All reals except -2, 0, and 2

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Divide Domain: All reals except 0, 3 and -3

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Adding Rational Expressions Need to reduce D: all reals except x = -2

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Adding Rational Expressions Need a Common Denominator D: All reals except x = -1/2 and x = 1

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