By Ron Larson
This market-leading textual content maintains to supply scholars and teachers with sound, constantly dependent reasons of the mathematical options. Designed for a two-term path, the recent 8th variation keeps the good points that experience made Algebra and Trigonometry an entire resolution for either scholars and teachers: fascinating purposes, state-of-the-art layout, and cutting edge expertise mixed with an abundance of rigorously written routines.
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Extra resources for Algebra and Trigonometry (Eighth Edition)
C. The domain of the expression xϩ2 xϪ3 is the set of all real numbers except x ϭ 3, which would result in division by zero, which is undefined. Now try Exercise 7. The quotient of two algebraic expressions is a fractional expression. Moreover, the quotient of two polynomials such as 1 , x 2x Ϫ 1 , xϩ1 or x2 Ϫ 1 x2 ϩ 1 is a rational expression. Simplifying Rational Expressions Recall that a fraction is in simplest form if its numerator and denominator have no factors in common aside from ± 1. To write a fraction in simplest form, divide out common factors.
Domain of an Algebraic Expression The set of real numbers for which an algebraic expression is defined is the domain of the expression. Two algebraic expressions are equivalent if they have the same domain and yield the same values for all numbers in their domain. For instance, ͑x ϩ 1͒ ϩ ͑x ϩ 2͒ and 2x ϩ 3 are equivalent because ͑x ϩ 1͒ ϩ ͑x ϩ 2͒ ϭ x ϩ 1 ϩ x ϩ 2 ϭxϩxϩ1ϩ2 Why you should learn it Rational expressions can be used to solve real-life problems. S. households banking and paying bills online from 2002 through 2007.
The square root sign implies only a positive root. When a negative root is needed, you must use the negative sign with the square root sign. Incorrect: Ί4 ϭ ± 2 Example 8 Correct: Ϫ Ί4 ϭ Ϫ2 and Ί4 ϭ 2 Evaluating Expressions Involving Radicals a. Ί36 ϭ 6 because 62 ϭ 36. b. Ϫ Ί36 ϭ Ϫ6 because Ϫ ͑Ί36͒ ϭ Ϫ ͑Ί62͒ ϭ Ϫ ͑6͒ ϭ Ϫ6. c. 5 5 ϭ because Ί125 64 4 4 3 3 ϭ 53 125 ϭ . 43 64 5 Ϫ32 ϭ Ϫ2 because ͑Ϫ2͒5 ϭ Ϫ32. d. Ί 4 Ϫ81 is not a real number because there is no real number that can be raised to the e.