SOLUTION: Find the values of A and B in the following partial fraction decomposition. 11x-2/x^2+x-6= A/x+3+B/x-2

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find the values of A and B in the following partial fraction decomposition. 11x-2/x^2+x-6= A/x+3+B/x-2      Log On


   

Question 39274: Find the values of A and B in the following partial fraction decomposition.
11x-2/x^2+x-6= A/x+3+B/x-2
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
The way we do this is to first multiply all terms by the lowest common denominator which is x^2+x-6 in this case...so we get (after multiplying)
11x-2 / x^2+x-6 = A/x+3 + B/x-2
11x - 2 = A(x - 2) + B(x + 3)
11x - 2 = Ax - 2A + Bx + 3B
11x - 2 = (A + B)x + (-2A + 3B)
Therefore
A + B = 11 and
-2A + 3B = -2
from which we solve and get
A = 7 and B = 4