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Partial Fractions?
Show step by step how:
[-1] / [(x + 1)(x^2 + 1)]
becomes:
(-1/2)[1/(x + 1)] + (1/2)[x/(x^2 + 1)] - (1/2)[1/(x^2 + 1)]
using partial fraction expansion
1 Answer
- cidyahLv 73 years ago
-1/((x+1)(x^2+1)) = A/(x+1) +(Bx+C)/(x^2+1)
multiply both sides by (x+1)(x^2+1)
-1 = A(x^2+1)+(Bx+C)(x+1)
Let x=-1
-1 = A(2) + (Bx+C)(0)
2A = -1
A=-1/2
Match the coefficients of x^2
0 = A+B
B = -A
B = 1/2
Match the coefficients of x
0 = B+C
C = -B = -1/2
A=-1/2; B=1/2 C=-1/2
-1/((x+1)(x^2+1)) = -1/(2(x+1)) + x/(2(x^2+1)) - 1/(2(x^2+1))
= -1/(2x+2) + x/(2x^2+2) - 1/(2x^2+2)
