mac1140_lecture4_2 - L4 1.5 Rational Expressions Example Find the domain of each rational expression and reduce it to the lowest terms Definition A

mac1140_lecture4_2 - L4 1.5 Rational Expressions Example...

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27 L4 §1.5 Rational Expressions Example. Find the domain of each rational expression and reduce it to the lowest terms. Definition . A rational expression is the quotient of two polynomials. The domain of an expression is set of all real numbers, for which the expression is defined. For a rational expression , the domain is the set of real numbers that do not make the denominator equal to 0. To find the domain of a rational expression , first determine all real values of x that make the denominator equal to 0, zeros of the denominator . Then, write: Domain: { zeros of the denominator} x x \ . Reducing Rational Expressions: Fundamental Principle of Fractions : ac a bc b = ( 0, 0) b c Note: Assume restrictions on the variables when writing a rational expression in lowest terms. 28 Warning: write the domain before canceling! a) 2 3 x x x Domain: b) 2 5 10 3 5 2 x x x = Domain: Multiplication and division : a c ac b d bd = a c a d b d b c ÷ = ( 0 0 0) b c d