The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
A common denominator for a set of fractions is simply the same (common) lower symbol (denominator). In practice the common denominator is chosen to be a number that is divisible by all of the denominators in an addition or subtraction problem. Thus for the fractions 2/3, 1/10, and 7/15, a common denominator is 30. Other common denominators are 60, 90, etc. The smallest of the common denominators is 30 and so it is called the least common denominator.
Similarly, the algebraic fractions x/2(x+2)(x-3) and 3x/(x+2)(x-1) have the common denominator of 2(x+2)(x-3)(x-1) as well as 4(x+2)(x-3)(x-1)(x2+4), etc. The polynomial of the least degree and with the smallest numerical coefficient is the least common denominator. Thus 2(x+2)(x-3)(x-1) is the least common denominator.
The most common use of the least common denominator (or L.C.D.) is in the addition of fractions. Thus, for example, to add 2/3, 1/10, and 7/15, we use the L.C.D. of 30 to write
2/3 + 1/10 + 7/15 as 2x10/3x10 + 1x3/10x3 + 7x2/15x2 which gives us 20/30 + 3/30 + 14/30 or 37/30
Similarly, we have
x/2(x+1)(x-3) + 3x/(x+2)(x-1) = x(x-1)/2(x+1)(x-3)(x-1) + 6x(x-3)/2(x+2)(x-1)(x-3)= [x(x-1)+6x(x-3)]/2(x+1)(x-3)(x-1)