1 The Set Of Real Numbers 2 Linear Equations And Inequalities 3 Graphing Linear Equations In Two Variables 4 Systems Of Linear Equations 5 Polynomials And Properties Of Exponents 6 Factoring Polynomials 7 Rational Expressions And Equations 8 Relations And Functions 9 More Equations And Inequalities 10 Radicals And Complex Numbers 11 Quadratic Equations And Functions 12 Exponential And Logarithmic Functions And Applications 13 Conic Sections 14 Binomial Expansions, Sequences, And Series A Additional Topics Appendix B Online Appendix B expand_more
7.1 Introduction To Rational Expressions 7.2 Multiplication And Division Of Rational Expressions 7.3 Least Common Denominator 7.4 Addition And Subtraction Of Rational Expressions 7.5 Complex Fractions 7.6 Rational Equations 7.7 Applications Of Rational Equations And Proportions Chapter Questions expand_more
Problem 1SP: Evaluate the expression for the given values of x. x − 3 x + 5 x = 2 Problem 2SP Problem 3SP: Evaluate the expression for the given values of x. x − 3 x + 5 x = 3 Problem 4SP: Evaluate the expression for the given values of x.
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Problem 5SP Problem 6SP: Identify the restricted values.
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Problem 7SP: Identify the restricted values.
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Problem 8SP: Identify the restricted values.
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Problem 9SP: Given
9. Factor the numerator and denominator.
Problem 10SP Problem 11SP Problem 12SP Problem 13SP Problem 14SP Problem 15SP Problem 1PE Problem 2PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 3PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 4PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 5PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 6PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 7PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 8PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 9PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 10PE: For Exercises 2–10, substitute the given number into the expression and simplify (if possible). (See... Problem 11PE: 11. A bicyclist rides 24 mi against a wind and returns 24 mi with the same wind. His average speed... Problem 12PE Problem 13PE: For Exercises 13–24, identify the restricted values. (See Examples 2–3.) 5 k + 2 Problem 14PE Problem 15PE Problem 16PE Problem 17PE: For Exercises 13–24, identify the restricted values. (See Examples 2–3.) m + 12 m 2 + 5 m + 6 Problem 18PE Problem 19PE: For Exercises 13–24, identify the restricted values. (See Examples 2–3.) x − 4 x 2 + 9 Problem 20PE: For Exercises 13–24, identify the restricted values. (See Examples 2–3.) x + 1 x 2 + 4 Problem 21PE Problem 22PE Problem 23PE: For Exercises 13–24, identify the restricted values. (See Examples 2–3.) t − 5 t Problem 24PE: For Exercises 13–24, identify the restricted values. (See Examples 2–3.) 2 w + 7 w Problem 25PE: 25. Construct a rational expression that is undefined for. (Answers will vary.)
Problem 26PE Problem 27PE: Construct a rational expression that is undefined for x = − 3 and x = 7 . (Answers will vary.) Problem 28PE: Construct a rational expression that is undefined for x = − 1 and x = 4 . (Answers will vary.) Problem 29PE: Evaluate the expressions for x = − 1 . a. 3 x 2 − 2 x − 1 6 x 2 − 7 x − 3 b. x − 1 2 x − 3 Problem 30PE: Evaluate the expressions for x = 4 . a. ( x + 5 ) 2 x 2 + 6 x + 5 b. x + 5 x + 1 Problem 31PE Problem 32PE Problem 33PE: For Exercises 33–42,
a. Identify the restricted values. b. Simplify the rational expression. (See... Problem 34PE: For Exercises 33–42,
a. Identify the restricted values. b. Simplify the rational expression. (See... Problem 35PE: For Exercises 33–42, a. Identify the restricted values.b. Simplify the rational expression. (See... Problem 36PE: For Exercises 33–42, a. Identify the restricted values.b. Simplify the rational expression. (See... Problem 37PE: For Exercises 33–42, a. Identify the restricted values.b. Simplify the rational expression. (See... Problem 38PE Problem 39PE Problem 40PE: For Exercises 33–42,
a. Identify the restricted values. b. Simplify the rational expression. (See... Problem 41PE: For Exercises 33–42, a. Identify the restricted values.b. Simplify the rational expression. (See... Problem 42PE Problem 43PE Problem 44PE Problem 45PE Problem 46PE Problem 47PE Problem 48PE Problem 49PE Problem 50PE Problem 51PE Problem 52PE Problem 53PE Problem 54PE Problem 55PE Problem 56PE Problem 57PE Problem 58PE: For Exercises 43–72, simplify the rational expression. (See Examples 5–6.)
58.
Problem 59PE Problem 60PE Problem 61PE Problem 62PE Problem 63PE Problem 64PE Problem 65PE Problem 66PE Problem 67PE Problem 68PE Problem 69PE Problem 70PE Problem 71PE Problem 72PE Problem 73PE: What is the relationship between x − 2 and 2 − x ? Problem 74PE: What is the relationship between w + p and − w − p ? Problem 75PE Problem 76PE Problem 77PE Problem 78PE Problem 79PE Problem 80PE Problem 81PE Problem 82PE Problem 83PE Problem 84PE Problem 85PE: For Exercises 75–86, simplify the rational expressions. (See Examples 7–8.)
85.
Problem 86PE Problem 87PE Problem 88PE Problem 89PE Problem 90PE Problem 91PE Problem 92PE Problem 93PE Problem 94PE Problem 95PE Problem 96PE Problem 97PE: For Exercises 87–100, simplify the rational expressions. 3 y − 3 x 2 x 2 − 4 x y + 2 y 2 Problem 98PE: For Exercises 87–100, simplify the rational expressions. 49 p 2 − 25 p q + 4 q 2 4 q − 14 p Problem 99PE: For Exercises 87–100, simplify the rational expressions. 2 t 2 − 3 t 2 t 4 − 13 t 3 + 15 t 2 Problem 100PE Problem 101PE Problem 102PE Problem 103PE: For Exercises 101–104, factor and simplify. z 2 − 16 z 3 − 64 Problem 104PE format_list_bulleted