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R Copyright © 2013, 2009, 2005 Pearson Education. Inc. Review of Basic Concepts Sections R.5–R.7

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-74 R.5 Rational Expressions R.6 Rational Exponents R.7 Radical Expressions Review of Basic Concepts R

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-75 Rational Expressions R.5 Rational Expressions Lowest Terms of a Rational Expression Multiplication and Division Addition and Subtraction Complex Fractions

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-76 Find the domain of the rational expression. Set the denominator equal to zero. R.5 Example 1 Finding the Domain (page 41)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-77 Write the rational expression in lowest terms. (a) R.5 Example 2(a) Writing Rational Expressions in Lowest Terms (page 42) Factor. Divide out the common factor.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-78 Write the rational expression in lowest terms. (b) R.5 Example 2(b) Writing Rational Expressions in Lowest Terms (page 42) Factor. Multiply numerator and denominator by –1. Divide out the common factor.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-79 R.5 Example 3(a) Multiplying or Dividing Rational Expressions (page 43) Multiply. Factor. Divide out common factors, then simplify.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-80 Multiply. R.5 Example 3(b) Multiplying or Dividing Rational Expressions (page 43) Factor. Multiply. Divide out common factors, then simplify.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-81 R.5 Example 3(c) Multiplying or Dividing Rational Expressions (page 43) Divide. Multiply by the reciprocal of the divisor. Factor. Multiply, then divide out common factors.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-82 R.5 Example 3(d) Multiplying or Dividing Rational Expressions (page 43) Multiply. Factor. Multiply, then divide out common factors.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-83 R.5 Example 4(a) Adding or Subtracting Rational Expressions (page 44) Add Find the LCD:

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-84 R.5 Example 4(b) Adding or Subtracting Rational Expressions (page 44) Add Find the LCD:

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-85 R.5 Example 4(c) Adding or Subtracting Rational Expressions (page 44) Subtract Find the LCD:

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-86 R.5 Example 5(a) Simplifying Complex Fractions (page 46) Simplify Multiply the numerator and denominator by the LCD of all the fractions, x 2.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-87 R.5 Example 5(b) Simplifying Complex Fractions (page 46) Simplify Multiply the numerator and denominator by the LCD of all the fractions, z(z + 1)(z – 1).

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-88 Rational Exponents R.6 Negative Exponents and the Quotient Rule Rational Exponents Complex Fractions Revisited

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-89 R.6 Example 1 Using the Definition of a Negative Exponent (page 50) Evaluate each expression. (a)(b)(c) (a) (b) (c)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-90 R.6 Example 1 Using the Definition of a Negative Exponent (cont.) Write the expression without negative exponents. (d) (e)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-91 R.6 Example 2 Using the Quotient Rule (page 51) Simplify each expression. (a) (b) (c) (d)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-92 R.6 Example 3(a) Using Rules for Exponents (page 51) Simplify.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-93 R.6 Example 3(b) Using Rules for Exponents (page 51) Simplify.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-94 R.6 Example 3(c) Using Rules for Exponents (page 51) Simplify.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-95 R.6 Example 4 Using the Definition of a 1/n (page 52) Evaluate each expression. (a)(b) (c)(d) (e)(f) (g)(h) not a real number

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-96 R.6 Example 5 Using the Definition of a m/n (page 53) Evaluate each expression. (a) (b) (c)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-97 R.6 Example 5 Using the Definition of a m/n (cont.) Evaluate each expression. (d) (e) (f) is not a real number because is not a real number.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-98 R.6 Example 6 Using the Rules for Exponents (page 54) Simplify each expression. (a) (b) (c)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-99 R.6 Example 6 Using the Rules for Exponents (cont.) Simplify each expression. (d) (e)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-100 R.6 Example 7 Factoring Expressions with Negative or Rational Exponents (page 54) Factor out the least power of the variable or variable expression. (a) (b) (c)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-101 R.6 Example 8 Simplifying a Fraction with Negative Exponents (page 55) Simplify. Write the result with only positive exponents. Definition of negative exponent Add fractions Multiply numerator and denominator by the LCD of the fractions. Factor Divide out the common factor

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-102 Radical Expressions R.7 Radical Notations Simplified Radicals Operations with Radicals Rationalizing Denominators

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-103 R.7 Example 1 Evaluating Roots (page 59) Write each root using exponents and evaluate. (a) (b) (c) (d) is not a real number.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-104 R.7 Example 1 Evaluating Roots (cont.) Write each root using exponents and evaluate. (e) (f)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-105 R.7 Example 2 Converting From Rational Exponents to Radicals (page 60) Write in radical form and simplify. (a) (b) (c) (d)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-106 R.7 Example 2 Converting From Rational Exponents to Radicals (cont.) Write in radical form and simplify. (e) (f) (g)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-107 R.7 Example 3 Converting From Radicals to Rational Exponents (page 60) Write in exponential form. (a) (b) (c) (d) (e)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-108 R.7 Example 4 Using Absolute Value to Simplify Roots (page 61) Simplify each expression. (a) (b) (c) (d)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-109 R.7 Example 4 Using Absolute Value to Simplify Roots (cont.) Simplify each expression. (e) (f) (g)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-110 R.7 Example 5 Simplifying Radical Expressions (page 62) Simplify each expression. (a) (b) (c)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-111 R.7 Example 5 Simplifying Radical Expressions (cont.) Simplify each expression. (d) (e) (f)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-112 R.7 Example 6 Simplifying Radicals (page 62) Simplify each radical. (a) (b) (c)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-113 R.7 Example 7 Adding and Subtracting Like Radicals (page 63) Add or subtract as indicated. (a) (b)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-114 R.7 Example 7 Adding and Subtracting Like Radicals (cont.) Add or subtract as indicated. (c)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-115 R.7 Example 8 Simplifying Radicals (page 64) Simplify each radical. (a) (b) (c)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-116 R.7 Example 9(a) Multiplying Radical Expressions (page 64) Find the product. Product of the sum and difference of two terms.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-117 R.7 Example 9(b) Multiplying Radical Expressions (page 64) Find the product. Simplify FOIL

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-118 R.7 Example 10 Rationalizing Denominators (page 65) Rationalize each denominator. (a) (b)

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-119 R.7 Example 11(a) Simplifying Radical Expressions with Fractions (page 65) Simplify the expression. Quotient ruleSimplify radicand. Rationalize denominator. Quotient rule

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-120 R.7 Example 11(b) Simplifying Radical Expressions with Fractions (page 65) Simplify the expression. Quotient rule Simplify the denominators. Write with a common denominator. Subtract the numerators.

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Copyright © 2013, 2009, 2005 Pearson Education. Inc. R-121 R.7 Example 12 Rationalizing a Binomial Denominator (page 66) Rationalize the denominator. Multiply the numerator and denominator by the conjugate of the denominator.

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