Rational Equations and Inequalities
Martin-Gay, Developmental Mathematics 2 14.1 – Simplifying Rational Expressions 14.2 – Multiplying and Dividing Rational Expressions 14.3 – Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominators 14.4 – Adding and Subtracting Rational Expressions with Dif ferent Denominators 14.5 – Solving Equations Containing Rational Expressions 14.6 – Problem Solving with Rational Expressions 14.7 – Simplifying Complex Fractions Chapter Sections
Simplifying Rational Expressions
Martin-Gay, Developmental Mathematics 4 Simplifying Rational Expressions RULE: 1.Factor the numerator and denominator. 2.Write a product of two rational expressions, one factor containing the GCF of the numerator and denominator, and the other containing the remaining factors. 3.Rewrite the factor containing the GCF as 1. 4.Multiply the remaining factors by 1.
Martin-Gay, Developmental Mathematics 5 Rational Expressions Q P Rational expressions can be written in the form where P and Q are both polynomials and Q 0. It is also called Algebraic Fractions. Examples of Rational Expressions 5 4 4 2 3 2 x x x 2 2 4 3 2 3 4 y xy x y x 4 3 2 x
Martin-Gay, Developmental Mathematics 6 Rational Expressions The following are NOT rational expressions x x 5 2 2 2 1 x x 1 4 2 3 x x
Martin-Gay, Developmental Mathematics 7 To evaluate a rational expression for a particular value(s), substitute the replacement value(s) into the rational expression and simplify the result. Evaluating Rational Expressions Example Evaluate the following expression for y = 2. y y 5 2 ) 2 2 ( 2 5 7 4 7 4
Martin-Gay, Developmental Mathematics 8 In the previous example, what would happen if we tried to evaluate the rational expression for y = 5? y y 5 2 5 2 5 5 0 3 This expression is undefined! Evaluating Rational Expressions
Martin-Gay, Developmental Mathematics 9 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 (the rational expression simply equals zero). Undefined Rational Expressions
Martin-Gay, Developmental Mathematics 10 Find any real numbers that make the following rational expression undefined. 45 15 4 9 3 x x x The expression is undefined when 15 x + 45 = 0. So the expression is undefined when x = 3. Undefined Rational Expressions Example
Martin-Gay, Developmental Mathematics 11 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 Expressions If P , Q , and R are polynomials, and Q and R are not 0, Q P QR PR Simplifying Rational Expressions
Martin-Gay, Developmental Mathematics 12 Simplifying a Rational Expression 1) Completely factor the numerator and denominator.
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- Fall '16
- Sherwin C. Lagrama
- Fractions, Fraction, Elementary arithmetic, Rational function