Question

Write the form of the partial fraction decomposition of the rational expression.

2x-4/x^2-1

Answer 1

(2x-1)/(x^2-1) = a/(x+1) + b/(x-1)

2x-1 = ax-a + bx + b

2 = a+b
-1 = -a+b
-----------add
1 = 2 b
b = 1/2
a = 2-b = 3/2
so
(3/2) / (x+1) + (1/2)/(x-1)