Beginning And Intermediate Algebra 5th Edition – Elayn Martin – Gay

7.1 | Rational Functions and Simplifying Rational Expressions As we reviewed in Chapter 1, a rational number is a number that can be written as a quo- tient of integers. A rational expression is also a quotient; it is a quotient of polynomials. 1 Find the Domain of a Rational ee Function. (> _ Rational Expression Simplify or Write Rational A rational expression is an expression that can be written in the form Expressions in Lowest Ne Terms.

() On Write Equivalent Rational where P and Q are polynomials and Q # 0. Expressions of the Form y dee £ aoe! ae ae a —a a : a tas 7 = a Rational Expressions al pPaie Use Rational Functions in a 3y ab 22 ee aaaliae Applications.

(> iz p>+2p+1 3x +7 The first rational expression (or fraction) above is a For a negative fraction 2: such as — > recall from Section 1.7 that Nee ie Ga -7 In general, for any fraction, —a_ a a Poe, oP b #0 This is also true for rational expressions. For example, reeOet 2). re setae z ——— Notice the parentheses. Rational expressions are sometimes used to describe functions. For example, we call +2 : eetight : the function f(x) = 3 3 rational function since is a rational expression.

= 1. Finding the Domain of a Rational Function © As with fractions, a rational expression is undefined if the denominator is 0. If a vari- able in a rational expression is replaced with a number that makes the denominator 0, we say that the rational expression is undefined for this value of the variable. For : ; : : : é example, the rational expression 3 is undefined when x is 3, because replacing x ae with 3 results in a denominator of 0.

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