Question

write out the form of the partial fraction expansion of the function. do not determine the numerical values of the coefficients: 1/(x^(3)+2x^(2)+x)

Answer 1

\[\frac{1}{x^3+2x^2+x}=\frac{1}{x(x^2+2x+1)}=\frac{1}{x(x+1)^2}\]
Hence the partial fraction expansion would be
\[\frac{A}{x}+\frac{B}{x+1}+\frac{C}{(x+1)^2}\]

Answer 2

wouldn't it be
\[\frac{A}{x}+\frac{B}{x+1}+\frac{Cx+D}{(x+1)^2}\]

Answer 3

No. You write \[Cx+D\] as the numerator when the quadratic in the denominator is not factorisable.

Answer 4

If the denominator is a perfect square (ax+b)^2, you split it as \[\frac{A}{ax+b}+\frac{B}{(ax+b)^2}\]

Answer 5

ok yes you are right
but i guess it wouldn't wrong to do what i have
since C would end up being 0 lol
i would be just causing more work for myself