SOLUTION: Please can you resolve this into partial fractions {{{x / (x-1)(x^2 - 4)}}} Thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please can you resolve this into partial fractions {{{x / (x-1)(x^2 - 4)}}} Thanks      Log On


   

Question 15694: Please can you resolve this into partial fractions
x+%2F+%28x-1%29%28x%5E2+-+4%29

Thanks
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2F+%28x-1%29%28x%5E2+-+4%29 = x%2F%28%28x-1%29%28x%2B2%29%28x-2%29%29
Let this be equal to a%2F%28x-1%29%2Bb%2F%28x%2B2%29%2Bc%2F%28x-2%29
= =
x%2F%28%28x-1%29%28x%2B2%29%28x-2%29%29
Since denominators are same , equating the numerators we get
a%28x%2B2%29%28x-2%29%2Bb%28x-1%29%28x-2%29%2Bc%28x-1%29%28x%2B2%29=x
since this is an identity , it is true for any value of x
hence take x=1,and -2 and 2 to get a ,b , c values
for x=1 ,we have
a(1+2)(1-2)=1
a = -1/3 similarly we get b=-2/12=-1/6 and c=2/4 = 1/2
hence
x+%2F+%28x-1%29%28x%5E2+-+4%29=