Download PDF by Bernard Kolman; Arnold Shapiro: College algebra

By Bernard Kolman; Arnold Shapiro

ISBN-10: 0124178979

ISBN-13: 9780124178977

A modern method of university algebra is supported via non-compulsory snap shots calculator fabric

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When rational expressions have the same denominator, the addition and subtrac­ tion rules are as follows. a b=a-b --c c c For example, 3_ _ 2_ _ 4_ _ s_ = 2 - 4 + s = _ + x- 1 x- 1 x- 1 x-1 x- l To add or subtract rational expressions with different denominators, we must first rewrite each rational expression as an equivalent one with the same denom- 34 THE FOUNDATIONS OF ALGEBRA inator as the others. Although any common denominator will do, we will con­ centrate on finding the least common denominator, or LCD, of two or more rational expressions.

X2 - l 8 3x - 9 2x x-1 44 · 2x + l (2x + I) (x - 2) 2_ x 46· _ + x - 2 x2 - x - 6 x-2 x 2x - I 2x - l 48 · 47· x3 - 4x x2 + x - 2 x2 + Sx + 6 x2 + 4x + 3 x 2x x+l l � so. + + 49. x + 2 x - 2 x2 - 4 x2 - l x2 + 3x - 4 In Exercises Sl-66 simplify the complex fraction and perform all indicated operations. I 2 x-l +x+ I 53. 52. 54. SI. l 2+ 1 -1 -­ x x x _ _ � ; SS. x2 - 16 x 4 a b S9. +! a b I y - -1 -! y 63. l y+ 1 +! l_ x+y a b --a-b a+b a2 - b2 S1. 1_ 2-1+! a x x - -x-2 x+2 60. k. +L x-2 x-2 61.

I = v'l = V(- 1)(- 1) COMPLEX NUMBERS = V-TV-1 = n vtx" + y" * x + y labl = -I that labl = lal lbl. ) One of the central problems in algebra is to find solutions to a given polynomial equation. This problem will be discussed in later chapters of this book. For now, observe that there is no real number that satisfies a simple polynomial equation like x2 = -4 since the square of a real number is always nonnegative. To resolve this problem, mathematicians created a new number system built upon an ..

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College algebra by Bernard Kolman; Arnold Shapiro


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