PartFrac - ...

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<?xml version="1.0" encoding="UTF-8"?> <Worksheet><Version major="6" minor="1"/><View-Properties><Zoom percentage="100"/></View-Properties><Styles><Layout alignment="left" bullet="none" linespacing="0.0" name="Heading 1" spaceabove="8.0" spacebelow="4.0"/><Layout alignment="left" bullet="none" firstindent="0.0" leftmargin="0.0" linebreak="space" linespacing="0.0" name="Normal" rightmargin="0.0" spaceabove="0.0" spacebelow="0.0"/><Layout alignment="centred" bullet="none" linespacing="0.5" name="Maple Output"/><Font background="[0,0,0]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" name="Maple Input" opaque="false" size="12"/><Font background="[0,0,0]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" name="Text" opaque="false" size="12" underline="false"/><Font background="[0,0,0]" executable="false" family="Times New Roman" foreground="[0,0,0]" name="2D Math" opaque="false" size="12"/><Font background="[0,0,0]" bold="true" family="Serif" name="Heading 1" opaque="false" size="18"/><Font background="[0,0,0]" family="Times New Roman" foreground="[0,0,255]" name="2D Output" opaque="false" readonly="true" size="12"/></Styles><Section><Title><Text-field alignment="centred" layout="Heading 1" style="Heading 1"><Font executable="false" size="24">Partial Fractions</Font></Text-field></Title><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" style="Text">A rational expression of the form P(x)/Q(x) where P(x) and Q(x) are polynomials, <Font bold="true">with degree(P)&lt;degree(Q)</Font>, can usually be decomposed into a sum of ratios of factors of Q(x). For example, </Text-field><Text-field layout="Normal" style="Text">if Q factors as</Text-field><Text-field layout="Normal" style="Text"/><Text-field alignment="centred" layout="Normal" style="Text"><Equation input-equation="Q(x) = (x-a[1])^s[1]*(x-a[2])^s[2]" style="2D Math">NiMvLUkiUUc2IjYjSSJ4R0YmKiYpLCZGKCIiIiZJImFHRiY2I0YsISIiJkkic0dGJkYvRiwpLCZGK EYsJkYuNiMiIiNGMCZGMkY2Riw=</Equation>. ..<Equation input-equation="(x-a[r])^(s[r])" style="2D Math">NiMpLCZJInhHNiIiIiImSSJhR0YmNiNJInJHRiYhIiImSSJzR0YmRio=</Equation></Text- field><Text-field layout="Normal" style="Text">where <Equation input- equation="s[n]" style="2D Math">NiMmSSJzRzYiNiNJIm5HRiU=</Equation> is the multiplicity of the factor, then </Text-field><Text-field alignment="centred" layout="Normal" style="Text"><Equation input-equation="P(x)/Q(x) = sum(sum(A[n, j]/ (x-a[1])^j, j = 1 . . s[n]), n = 1 . . r)" style="2D Math">NiMvKiYtSSJQRzYiNiNJInhHRiciIiItSSJRR0YnRighIiItSSRzdW1HNiRJKnByb3RlY3RlZEdGM UkoX3N5c2xpYkdGJzYkLUYvNiQqJiZJIkFHRic2JEkibkdGJ0kiakdGJ0YqKSwmRilGKiZJImFHRic2I0Yq Ri1GO0YtL0Y7O0YqJkkic0dGJzYjRjovRjo7RipJInJHRic=</Equation> (*)</Text- field><Text-field alignment="centred" layout="Normal" style="Text"/><Text-field layout="Normal" style="Text">for some <Equation input-equation="A[n,j]" style="2D Math">NiMmSSJBRzYiNiRJIm5HRiVJImpHRiU=</Equation>. To determine <Equation input-
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This note was uploaded on 12/02/2009 for the course MATH 352 taught by Professor Staff during the Spring '08 term at University of Delaware.

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PartFrac - ...

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