7.1 - Math096 Chapter 7 7.1 Rational Functions and...

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Unformatted text preview: Math096: Chapter 7 7.1: Rational Functions and Simplifying Rational Expressions Rational expressions can be written in the form EP— where P and Q are both polynomials and Q” Examples of Rational Expressions R ' V = h. m N! fax +236 4 x24x+3y 3x2 :Dowo—in :- #IXFS: 4;}? 5 ___2xj —23xy+4y 4 erx] K” 411 Rania D The aluate a ational expression for a particu at value, substitute the replacement value into the rational expression and simplify the result. Evaluate the following expression for y = —2 [Ci 7;" fii — 2 —- 21 ~ 1 “ 5 + y __ 6‘... \ Ll’ -é 2.3 Q [:5— Undefined Rational Expressions We have to be able to determine when a rational expression is undefined. A rational expression is undefined when the denominator is equal to zero. The numerator being equal to zero is okay (as the rational expression simply equals zero). Example: Find any real numbers that make the following rational 3 16X+ 63:0 expression undefined. 2w _ Li .. le+45 M =— "‘f") '8' X = -—3 To find the domain of a function defined b an e nation: I. Start with the domain as the set of real numbers. 2. If the equation has a denominator, exclude any numbers that give a zero denominator. {>4 X % ———— 3 3 SUan "1'31“ ‘i' 3. If the equation has a radical of even index, exclude any numbers that cause the expression inside the radical to be negative. \Jx-l < > | ’2’») 0 Find the domain of a rational function. 0 x mhfikq . lelefi — : . X 01"-: x (x+2)(X-') )lxl 7: R. V; o, -a ’ ' Simplifying Rational Expressions Simplifying a rational expression means writing it in lowest terms or simplest form. To do this, we need to use the Fundamental Principle of Rational Exgressions If P, Q, and R are polynomials, and Q and R are not 0, 3:5 QR Q Simplifying Rational Expressions 1) Completely factor the numerator and denominator. 2) Apply the Fundamental Principle of Rational Expressions to eliminate common factors in the numerator and denominator. Warning! Only common FACTORS can be eliminated from the numerator and denominator. Make sure any expression you eliminate is a factor. Simplifl the following expressions. 7x+35_ “”499 x2+5xfi XCM [it -—--—_' X 3x3 fix ~33 ~47; xgzj+€)—el_(7—3+5) ...
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