SOLUTION: Find A, B, and C such that (x-1)/(x+1)(x-2)^2 = A/(x+1) + B/(x-2) + C/(x-2)^2

Question 983910: Find A, B, and C such that (x-1)/(x+1)(x-2)^2 = A/(x+1) + B/(x-2) + C/(x-2)^2
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
(x-1)/(x+1)(x-2)^2 = A/(x+1) + B/(x-2) + C/(x-2)^2
Multiply everything out with the common denominator of (x+1)(x-2)^2.
Then (x-1)/(x+1)(x-2)^2 = A(x-2)^2 + B(x+1)(x-2) + C((x+1)
Now make one of those parentheses on the right =0.
Let x=2
Then C(x+1)=x-1, if x=2 ;;; A and B both =0.
3C=1 ; c=(1/3)
Let x=-1
-2=9A
A=(-2/9)
;
x=0
-1=4A-2B+C
but -1=(-8/9)-2B+1/3
-1=(-5/9)-2B
2B=4/9
B=2/9
;
can check with a different x. Try 5
4=9*(-2/9)+18(2/9)+6(1/3)=-2+4+2=4, so it checks.
;
It is -2/9(x+1) + 2/9(x-2)+ 1/3(x-2)^2

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