Math  /  Algebra

Questionfind A,B,CA, B, C, and DD using partial Lractions ss41=As1+Bs+1+cx+1s2+1\frac{s}{s^{4}-1}=\frac{A}{s-1}+\frac{B}{s+1}+\frac{c x+1}{s^{2}+1}

Studdy Solution
Equate coefficients from both sides of the equation:
1. Coefficient of s3s^3: A+B+C=0A + B + C = 0
2. Coefficient of s2s^2: AB+D=0A - B + D = 0
3. Coefficient of ss: A+BC=1A + B - C = 1
4. Constant term: ABD=0A - B - D = 0

Solve these simultaneous equations to find AA, BB, CC, and DD.
Solution for the coefficients:
1. From equation 1: A+B+C=0A + B + C = 0
2. From equation 2: AB+D=0A - B + D = 0
3. From equation 3: A+BC=1A + B - C = 1
4. From equation 4: ABD=0A - B - D = 0

Solving these equations, we find: - A=12A = \frac{1}{2} - B=12B = \frac{1}{2} - C=1C = -1 - D=0D = 0
Thus, the values are: A=12,B=12,C=1,D=0 A = \frac{1}{2}, \quad B = \frac{1}{2}, \quad C = -1, \quad D = 0

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