Posted by **chrystabelle** on Thursday, February 16, 2012 at 5:19am.

express x-1/(x+1)(x-2)^2 into partial fractions

- maths -
**Reiny**, Thursday, February 16, 2012 at 8:34am
let

(x-1)/((x+1)(x-2)^2) = A/(x-1) + B/(x-2) + C/(x-2)^2

multiply both sides by (x+1)(x-2)^2

A(x-2)^2 + B(x-2)(x+1) + C(x+1) = x-1

let x = 2, ---> 3C = 1 or C=13

let x = -1 ---> 9A + -2 or A = -2/9

let x = 0 ----> 4A - 2B + C = -1

4(-2/9) - 2B + 1/3 = -1

times 9

-8 - 18B + 3 = -9

B = 2/9

so (x-1)/(x-2)^2 = -2/(9(x+1)) + 2/(9(x-2)) + 1/(3(x-2)^2)

verified with Wolfram:

http://www.wolframalpha.com/input/?i=%28x-1%29%2F%28%28x%2B1%29%28x-2%29%5E2%29

- typo - maths -
**Reiny**, Thursday, February 16, 2012 at 8:36am
in the middle of the solution above the line should read:

et x = 2, ---> 3C = 1 or C=1/3

## Answer this Question

## Related Questions

- Math - Express 13-15x^2/(x^2-1)(x 3) into partial fractions
- maths - Resolve 3x/x^2-x-12 into partial fractions
- Binomial - Help me on this one :( Express y= (7-3x-x^2)/[((1-x)^2)(2+x)] in ...
- Maths - Resolve into partial fractions: (x+3)(x+1)/ x(x^2+x+1) Can anyone please...
- Math- Partial Fractions - Decompose the following into partial fractions after ...
- math - Express (5x+2)/(2x-1)(x+1) into partial fractions and hence expand the ...
- Maths-Integration by Partial Fraction - Use integration by partial fractions to ...
- math/algebra - Express x^2 - 3x/x^2 - 1 As partial fractions
- math/algebra - Express x^2 - 3x x^2 - 1 As partial fractions
- math - Express (15x^2+5x+2)/(2-x)(1+2x^2) in partial fractions.

More Related Questions