By Earl Swokowski, Jeffery A. Cole
The most recent version 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 apparent, the time-tested workout units function quite a few functions, its uncluttered format is attractive, and the trouble point of difficulties is suitable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage version, 12E, successfully prepares scholars for additional classes in arithmetic via its very good, time-tested challenge units.
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Extra resources for Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition
Since division by zero is not allowed, the domain of p͞q consists of all real numbers except those that make the denominator zero. Two illustrations are given in the chart. 4 Fractional Expressions 41 In most of our work we will be concerned with rational expressions in which both numerator and denominator are polynomials in only one variable. 1, replacing the letters a, b, c, and d with polynomials. The following property is of particular importance, where bd 0: ad a d a a ϭ и ϭ и1ϭ bd b d b b We sometimes describe this simplification process by saying that a common nonzero factor in the numerator and denominator of a quotient may be canceled.
The only difference is that we use factorizations of polynomials instead of integers. EXAMPLE 3 Sums and differences of rational expressions Perform the operations and simplify: 6 5 2 ϩ Ϫ x͑3x Ϫ 2͒ 3x Ϫ 2 x 2 The denominators are already in factored form. The lcd is x 2͑3x Ϫ 2͒. To obtain three quotients having the denominator x 2͑3x Ϫ 2͒, we multiply the numerator and denominator of the first quotient by x, those of the second by x 2, and those of the third by 3x Ϫ 2, which gives us SOLUTION 6 5 2 6 x 5 x2 2 3x Ϫ 2 ϩ Ϫ 2ϭ и ϩ и 2Ϫ 2и x͑3x Ϫ 2͒ 3x Ϫ 2 x x͑3x Ϫ 2͒ x 3x Ϫ 2 x x 3x Ϫ 2 ϭ 6x 5x 2 2͑3x Ϫ 2͒ ϩ 2 Ϫ x ͑3x Ϫ 2͒ x ͑3x Ϫ 2͒ x 2͑3x Ϫ 2͒ ϭ 6x ϩ 5x 2 Ϫ 2͑3x Ϫ 2͒ x 2͑3x Ϫ 2͒ ϭ 5x 2 ϩ 4 .
1 (g) The quotient of r and s is at least 5 . (h) The reciprocal of f is at most 14. ( i ) The absolute value of x is less than 4. Exer. 7–8: Express the statement as an inequality. 7 (a) x is negative. 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.