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Rational Expressions and EquationsStudy Strategy –Preparing for a Cumulative Exam•Preparing for a Cumulative Review Section 7.1 –Rational Expressions and FunctionsConcept –Rational Expressions Example –Rational Expressions Concept –Values for Which a Rational Expression is Undefined To find the values for which a rational expression is undefined, we set the denominator equal to 0 and solve the resulting equation. These solutions are the values for which the expression is undefined. Example –Values for Which a Rational Expression is Undefined Find the values for which the rational expression is undefined: The expression is undefined for x=3,6. Concept –Simplifying a Rational Expression to Lowest Terms To simplify a rational expression to lowest terms, we first factor the numerator and denominator. Then we may divide out common factors in the numerator and denominator. Example –Simplifying a Rational Expression to Lowest Terms Simplify to lowest terms: Concept –Factors That Are Opposites Two expressions of the form a-b and b-a are opposites. The rational expression simplifies to equal -1,as any fraction whose numerator is the opposite of its denominator is equal to -1. Example –Factors That Are Opposites Simplify to lowest terms: Section 7.2 –Multiplication and Division of Rational ExpressionsConcept –Multiplying Rational Expressions To multiply two rational expressions, factor each numerator and denominator completely. Divide out factors that are common to a numerator and a denominator and multiply the remaining factors, leaving the numerator and denominator in factored form. Example –Multiplying Rational Expressions Concept –Dividing Rational Expressions To divide a rational expression by another rational expression, replace the divisor by its reciprocal and then multiply. Example –Dividing Rational Expressions |