SOLUTION: Consider the rational function f(x)= x-1/x^2-4 Find the partial fraction expansion of f.

Algebra ->  Rational-functions -> SOLUTION: Consider the rational function f(x)= x-1/x^2-4 Find the partial fraction expansion of f.      Log On


   

Question 1015205: Consider the rational function f(x)= x-1/x^2-4 Find the partial fraction expansion of f.
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
What you need to do is find A and B such that
%28x-1%29%2F%28x%5E2-4%29+=+A%2F%28x%2B2%29+%2B+B%2F%28x-2%29
After multiplying by the common denominator
x-1 = A(x-2) + B(x+2)
x-1 = Ax - 2A + Bx + 2B
this means
A + B = 1 and
2B - 2A = -1
B - A = -1/2
Now add these and get
2B = 1/2
B = 1/4
A = 3/4