precalc
posted by Robert .
Write the partial fraction decomposition of the rational expression.
6x^2+1/x^2(x1)^2

Because of the duplication of factors we could have
A/x + B/x^2 + C/(x1) + D/(x1)^2 = (6x^2 + 1)/(x^2(x1)^2)
multiply by x^2(x1)^1
A(x1)^2 + Bx(x1)^2 + Cx^2(x1) + Dx^2 = 6x^2 + 1
let x=0 > A = 1
let x=1 > D = 7
then (x1)^2 + Bx(x1)^2 + Cx^2(x1) + 7x^2 = 6x^2 + 1
let x=2 > 1 + 2B + 4C + 28 = 24+1
or B + 2C = 2 (#1)
let x = 1 > 4  4B  2C + 7 = 7
or 2B + C = 2 (#2)
2 (#1)  #2
3C = 6
C = 2
then B = 2 form #1
so (6x^2 + 1)/(x^2(x1)^2)
= 1/x^2 + 2/x  2/(x1) + 7/(x1)^2 
Looks like it should have said
A/x^2 + B/x + C/(x1) + D/(x1)^2 = (6x^2 + 1)/(x^2(x1)^2)
but the solution from there on is correct.