Question

Partial fraction decomposition: \(\dfrac{2x^2+7x-1}{x^3+x^2-x-1}\) I've factored the denominator into \((x^2-1)(x+1)\), and set up my system of equations to solve for A, B, and C, but the system doesn't have a solution (unless I made an error somewhere).

Answer 1

I got \(\dfrac{A}{x+1}+\dfrac{Bx+C}{x^2-1}\), and ended up with the system A+B=2, B+C=7, C-A=-1, which reduces to 0=6

Answer 2

you must fac den to (x+1)^2(x-1)
and then a/x+1+b/(x+1)2+c/x-1
b=3 , c=2 , a=0

Answer 3

Oh, duh, \(x^2-1\) isn't fully factored. I'm dumb. Thanks!

Answer 4

3/(x+1)^2+2/(x-1)