Posted by Robert on Sunday, December 4, 2011 at 9:54pm.
Because of the duplication of factors we could have
A/x + B/x^2 + C/(x-1) + D/(x-1)^2 = (6x^2 + 1)/(x^2(x-1)^2)
multiply by x^2(x-1)^1
A(x-1)^2 + Bx(x-1)^2 + Cx^2(x-1) + Dx^2 = 6x^2 + 1
let x=0 --> A = 1
let x=1 --> D = 7
then (x-1)^2 + Bx(x-1)^2 + Cx^2(x-1) + 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(x-1)^2)
= 1/x^2 + 2/x - 2/(x-1) + 7/(x-1)^2
Looks like it should have said
A/x^2 + B/x + C/(x-1) + D/(x-1)^2 = (6x^2 + 1)/(x^2(x-1)^2)
but the solution from there on is correct.
Related Questions
precalc/trig - Write the partial fraction decomposition of the rational ...
Math - Write the partial fraction decomposition of the rational expression. (80-...
Calculus - Write the form of the partial fraction decomposition of the rational ...
algebra - write the partial fraction decomposition of the rational expression ax...
Algebra-Partial Fractions - Can you please help me with the following questions ...
Partial Decompostion Fractions - Can you please help me with the following ...
Math grade 12 - write the partial fraction decomposition of the following ...
Trig - How would you write the partial fraction decomposition of the rational ...
pre calc - write the form of the partial decomposition for the given rational ...
Pre-Calculus(Help) - Partial Fraction of the Rational Expression: x^2+x+8/x^3+x
For Further Reading
