1. ## Partial Fractions

I understand the main idea about partial fractions. We were given this 'challenge problem', and this definitely doesn't look
what are the coefficients A B C D E for

(5x^4 - 10x^3 + x^2 - 24x + 18) /
((x-4) ((x^2 +1)^2))

using: A/x-4 + Bx+C/x^2+1 + Dx+E/ ((x^2+1)^2)

2. Originally Posted by C.C.
I understand the main idea about partial fractions. We were given this 'challenge problem', and this definitely doesn't look
what are the coefficients A B C D E for

(5x^4 - 10x^3 + x^2 - 24x + 18) /
((x-4) ((x^2 +1)^2))

using: A/x-4 + Bx+C/x^2+1 + Dx+E/ ((x^2+1)^2)
HI

$\displaystyle \frac{5x^4-10x^3+x^2-24x+18}{(x-4)(x^2+1)^2}=\frac{A}{x-4}+\frac{Bx+C}{x^2+1}+\frac{Dx+E}{(x^2+1)^2}$

Multiply the whole thing by (x-4)

$\displaystyle \frac{5x^4-10x^3+x^2-24x+18}{(x^2+1)^2}=A+\left(\frac{Bx+C}{x^2+1}+\fra c{Dx+E}{(x^2+1)^2}\right)(x-4)$

Substitute x=4 ,you can get A . THen substitute other values : 0 , 1 , -1 etc , values which make your calculation convenient . You will need to solve these simultaneous equations to get the rest . I haven tried yet , you give it a try and see whether it works or not . GOod luck .