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How to express this in partial fractions?
Hi, I'm not sure how to express this in partial fractions:
2x-1/(x+1)^2
I have to do it in the form A/(x+1) + B/(x+1)^2
This doesn't make any sense to me, I have tried countless times to do it, your help would be much appreciated! Thank you
1 Answer
- MathLv 77 years agoFavorite Answer
You have (2x-1)/(x+1)^2 = A/(x+1) + B/(x+1)^2
Factoring RHS we get
(A(x + 1)^2 + B(x + 1))/(x + 1)^3 =(2x-1)/(x+1)^2
We now cross multiply
A(x + 1)^4 + B(x + 1)^3 = (x + 1)^(3)(2x - 1)
Factoring out (x + 1)^3 on both sides results in
A(x + 1) + B = (2x - 1)
Expanding LHS results in
Ax + (A + B) = 2x - 1
This implies A = 2 and A + B = -1
So B = -3
Therefore the partial fraction expansion is
2/(x+1) -3/(x+1)^2
Done!
