Asked by Anonymous
Write the form of the partial fraction decomposition of the rational expression.
2x-4/x^2-1
2x-4/x^2-1
Answers
Answered by
Damon
(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)
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)
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