Rational Function into Partial Fraction

Question

HI Looking to make 72/36s+s^3 into partial fraction. 

 

Can find the value of A ok but can't seem to cancel out A value to find B. Expanding the denominator I got s(s^2+36), then when I come to cancel out A value a squared value + 36 will not =0.

 

Thanks for your help in advance.

 

Michael

Answer 1

Not sure exactly what you have but the expression should look like:

 

72/[s(s² + 36)] = A/s + (Bs+C)/(s² + 36)

 

then you are solving for A,B, and C.

 

Is this what you tried?

 

 

Answer 2

72/(36s+s³) = 72/s(36+s²) = 72/s(s+6i)(s-6i)

 

We want:

 

     72/s(s+6i)(s-6i) = A/s + B/(s+61) + C/(s-6i)

     72/s(s+6i)(s-6i) = [ A(s+6i)(s-6i) + Bs(s-6i) + Cs(s+6i) ] / s(s+6i)(s-6i)

 

     72 = A(s+6i)(s-6i) + Bs(s-6i) + Cs(s+6i) 

 

For s=0:

     72 = A*(-36i²)

     72 = A*36

     2 = A

 

For s = s+6i:

     72 = C*6i*12i

     72 = C*(-72)

     -1 = C

 

For s = -6i:

     72 = b*(-6i)*(-12i)

     72 = -c*72

     -1 = C

 

72/(36s+s³) = 2/s - 1/(s+6i) - 1/(s-6i)

 

To check it, put the RHS over the common denominator.

 

Answer 3

A/s+ (Bs+C)/(s^2 +36)= 72/s(s^2 +36)

 

As^2 +36A+Bs^2 +Cs=72

A+B=0

C=0

36A=72

A=2

B=-2

 

So we have    2/s - 2s/(s^2+36)=  72/s(s^2+36)