Chapter 12 : Radicals and Connections to Geometry : 12.2 Operations with Radical Expressions


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	12.1 Functions Involving Square Roots 12.2 Operations with Radical Expressions 12.3 Solving Radical Equations 12.4 Rational Exponents 12.5 Completing the Square 12.6 The Pythagorean Theorem and Its Converse 12.7 The Distance Formula 12.8 The Midpoint Formulas 12.9 Logical Reasoning: Proof

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	Chapter 12 : Radicals and Connections to Geometry 12.2 Operations with Radical Expressions

12.2 Problem Solving Help Help for Exercises 41-52 on page 702 Exercises 41-46 involve rational expressions that contain a single radical term in the denominator. The examples below are similar. Example 1 Simplify Solution: Example 2 Simplify Solution: Notice that in Example 1, the final result is . This result does not simplify to because the numerator contains a radical while the denominator does not. In Exercises 47-52, you are given expressions in the denominator of the form . Refer to the Study Tips on page 699. Multiplying by an appropriate radical expression with a value of one will eliminate the radical in the denominator. In general, . After this step, if possible identify common factors between the numerator and denominator and simplify the resulting expression.