By Earl Swokowski, Jeffery A. Cole
The newest variation within the hugely revered Swokowski/Cole precalculus sequence keeps the weather that experience made it so well-liked by teachers and scholars alike: its exposition is obvious, the time-tested workout units characteristic quite a few purposes, its uncluttered format is attractive, and the trouble point of difficulties is suitable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage variation, 12E, successfully prepares scholars for extra classes in arithmetic via its very good, time-tested challenge units.
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Extra info for Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition
To simplify a rational expression, we factor both the numerator and the denominator into prime factors and then, assuming the factors in the denominator are not zero, cancel common factors, as in the following illustration. ILLUS TRATION Simplified Rational Expressions if x 2 ͑3x ϩ 1͒͑x Ϫ 2͒ b 3x ϩ 1 3x Ϫ 5x Ϫ 2 ϭ ϭ if x 2͞3 x2 Ϫ 4 ͑x ϩ 2͒͑x Ϫ 2͒ xϩ2 2 2 2 Ϫ x Ϫ 3x Ϫ͑3x ϩ x Ϫ 2͒ ͑3x Ϫ 2͒͑x ϩ 1͒ b xϩ1 ϭ ϭ Ϫ ϭϪ 6x2 Ϫ x Ϫ 2 6x2 Ϫ x Ϫ 2 ͑3x Ϫ 2͒͑2x ϩ 1͒ 2x ϩ 1 2 if x 1 2 5, x Ϫ4 b ͑x ϩ 8x ϩ 16͒͑x Ϫ 5͒ ͑x ϩ 4͒ ͑x Ϫ 5͒ xϩ4 ϭ ϭ ͑x2 Ϫ 5x͒͑x2 Ϫ 16͒ x͑x Ϫ 5͒͑x ϩ 4͒͑x Ϫ 4͒ x͑x Ϫ 4͒ 2 As shown in the next example, when simplifying a product or quotient of rational expressions, we often use properties of quotients to obtain one rational expression.
Exer. 9–14: Rewrite the number without using the absolute value symbol, and simplify the result. 9 (a) ͉ Ϫ3 Ϫ 2 ͉ (b) ͉ Ϫ5 ͉ Ϫ ͉ 2 ͉ (c) ͉ 7 ͉ ϩ ͉ Ϫ4 ͉ (c) q is less than or equal to . 10 (a) ͉ Ϫ11 ϩ 1 ͉ (b) ͉ 6 ͉ Ϫ ͉ Ϫ3 ͉ (c) ͉ 8 ͉ ϩ ͉ Ϫ9 ͉ (d) d is between 4 and 2. 11 (a) ͑Ϫ5͉͒ 3 Ϫ 6 ͉ (b) ͉ Ϫ6 ͉͑͞Ϫ2͒ (c) ͉ Ϫ7 ͉ ϩ ͉ 4 ͉ (e) t is not less than 5. 12 (a) ͑4͉͒ 6 Ϫ 7 ͉ (b) 5͉͞ Ϫ2 ͉ (c) ͉ Ϫ1 ͉ ϩ ͉ Ϫ9 ͉ (b) y is nonnegative. 7 Ϫ 23 ͉ (c) ͉ 51 Ϫ 13 ͉ Exer. 15 – 18: The given numbers are coordinates of points A, B, and C, respectively, on a coordinate line.
025 I3 or 2. 025 E I3 or 2. 48 ϫ 10Ϫ4 Many calculators use scientific form in their display panels. For the number c ϫ 10n, the 10 is suppressed and the exponent is often shown preceded by the letter E. For example, to find ͑4,500,000͒2 on a scientific calculator, we could enter the integer 4,500,000 and press the x 2 (or squaring) key, obtaining a display similar to one of those in Figure 6. 025 ϫ 1013. Thus, ͑4,500,000͒2 ϭ 20,250,000,000,000. Calculators may also use scientific form in the entry of numbers.
Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition by Earl Swokowski, Jeffery A. Cole