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help with partial fractions?
I need help on my pre-calculus study guide
the question is write the partial fraction decomposition of the rational expression
the problem is
11x+1/ (x-1)(x^2+x+1)
1 Answer
- MechEng2030Lv 78 years ago
(11x + 1)/(x - 1)(x^2 + x + 1) = A/(x - 1) + (Bx + C)/(x^2 + x + 1)
= A(x^2 + x + 1) + (Bx + C)(x - 1) = 11x + 1
x^2(A + B) + x(C - B + A) + A - C = 11x + 1
A + B = 0
C - B + A = 11
A - C = 1
2A - B = 12
3A = 12 => A = 4, B = -4, C = 3
Therefore:
(11x + 1)/(x - 1)(x^2 + x + 1) = 4/(x - 1) + (-4x + 3)/(x^2 + x + 1)