decompose-at-simple-element-the-fraction-F-x-1-x-7-x-2-1-2-

Question Number 59580 by maxmathsup by imad last updated on 12/May/19

d e c o m p o s e a t s i m p l e e l e m e n t t h e f r a c t i o n

F (x) = \frac{1}{x^{7} {(x^{2} - 1)}^{2}}

Commented by malwaan last updated on 12/May/19

I n e e d s o m e t i m e!

Answered by MJS last updated on 13/May/19

F (x) = \frac{a}{{(x - 1)}^{2}} + \frac{b}{{(x + 1)}^{2}} + \frac{c}{x - 1} + \frac{d}{x + 1} + \frac{e}{x} + \frac{f}{x^{2}} + \frac{g}{x^{3}} + \frac{h}{x^{4}} + \frac{i}{x^{5}} + \frac{j}{x^{6}} + \frac{k}{x^{7}}

the numerator of this fraction = N

N - 1 = 0

\Rightarrow the constant factors on the left handed side

are zero :

x^{10} : c + d + e = 0

x^{9} : a + b + c - d + f = 0

x^{8} : 2 (a - b - e) - c - d + g = 0

x^{7} : a + b - c + d - 2 f + h = 0

x^{6} : e - 2 g + i = 0

x^{5} : f - 2 h + j = 0

x^{4} : g - 2 i + k = 0

x^{3} : h - 2 j = 0

x^{2} : i - 2 k = 0

x^{1} : j = 0

x^{0} : k - 1 = 0

\Rightarrow a = \frac{1}{4}; b = - \frac{1}{4}; c = - 2; d = - 2; e = 4;

f = 0; g = 3; h = 0; i = 2; j = 0; k = 1

\Rightarrow

F (x) = \frac{1}{4 {(x - 1)}^{2}} - \frac{1}{4 {(x + 1)}^{2}} - \frac{2}{x - 1} - \frac{2}{x + 1} + \frac{4}{x} + \frac{3}{x^{3}} + \frac{2}{x^{5}} + \frac{1}{x^{7}}

Commented by ajfour last updated on 12/May/19

FABULOUS S i r!

Commented by malwaan last updated on 15/May/19

t h a n k s s i r!

Commented by MJS last updated on 13/May/19

yes, just a typo . I corrected .

thank you!

Facebook Tweet Pin