SOLUTION: What is the value of A, B, and C if: (A / (x+1)) + (B / (x+2)) + (C / (x-3)) = (2x²-6x +6) / ((x-1)(x-2)(x-3))

Algebra ->  Expressions -> SOLUTION: What is the value of A, B, and C if: (A / (x+1)) + (B / (x+2)) + (C / (x-3)) = (2x²-6x +6) / ((x-1)(x-2)(x-3))      Log On


   

Question 1184482: What is the value of A, B, and C if:
(A / (x+1)) + (B / (x+2)) + (C / (x-3)) = (2x²-6x +6) / ((x-1)(x-2)(x-3))
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

I'll bet this was a partial fraction problem and you copied the wrong
denominators either on the left side or the right side. However, I'll
solve the problem that you posted anyway:

Substituting x=0 and simplifying



A%2F%281%29+%2B+B%2F%282%29+%2B+C%2F%28-3%29+=+%280-0%2B6%29+%2F+%28-1%29%28-2%29%28-3%29%29

A+%2B+B%2F2+-+C%2F3+=+6%2F%28-6%29

A+%2B+B%2F2+-+C%2F3+=+-1

6A+%2B+3B+-+2C+=+-6

Substituting x=4 and simplifying



A%2F5+%2B+B%2F6+%2B+C%2F1+=+%2832-24%2B6%29+%2F+%28%283%29%282%29%281%29%29

A%2F5+%2B+B%2F6+%2B+C+=+14%2F6

6A%2B5B%2B30C=70

Substituting x=-3 and simplifying





-A%2F2+-+B+-+C%2F6+=+%2818%2B18%2B6%29+%2F+%28-120%29

-A%2F2+-+B+-+C%2F6+=+42%2F%28-120%29

-A%2F2+-+B+-+C%2F6+=+-42%2F120

-A%2F2+-+B+-+C%2F6+=+-7%2F20

-30A+-+60B-10C+=+-21

30A+%2B+60B%2B10C+=+21

Solve the system:

system%286A+%2B+3B+-+2C+=+-6%2C6A%2B5B%2B30C=70%2C+30A+%2B+60B%2B10C+=+21%29

Solve that system and get 

A+=+-1%2F4, B+=+2%2F25, C+=+237%2F100

Then your answer would be:





But I'll bet you you copied those denominators wrong!!!!

Edwin