By Bernard Kolman; Arnold Shapiro
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 ..
College algebra by Bernard Kolman; Arnold Shapiro