Partial Fractions

[Frogger888]

Can somebody check my work
I have

s/[(s+2)(s^2+4)]

so I take A/(s+2) + B/(s^2+4)

s=A(s^2+4)+B(s+2)
so
Bs=s B=1 then I plug in 1 for B throughout the equation and get A =-1/2

Did I do this right?

 

[galactus]

No, not quite.

Because of the s^2+4 , you should use the form:

\(\displaystyle \L\\\frac{As+B}{s^{2}+4}+\frac{C}{s+2}=s\)

Now, can you take it from there?.

 

[daon]

Try evaluating your original equation at a few numbers (plug in for s) and then your new equation with your found A and B at the same values for s.

If they are different, chances are your found numbers are wrong. I can tell you that you made a mistake however. It is not \(\displaystyle \frac{B}{s^2+4}\).

 

[Frogger888]

I am getting

B=1/4 A=3/8 and C=-1/8

 

[galactus]

Sorry,

Try this. It's one way:

\(\displaystyle (Ax+B)(x+2)+C(x^{2}+4)=x\)

Expand and compare like coefficients. Solve the small system for A, B, and C.

 

[Frogger888]

Finally I got it I got c=-1/4 b=1/2 a=1

I just got stuck on the algebra parts
Thanks

 

[pka]

This is the decomposition I get:
\(\displaystyle \L
\frac{{ - 1}}{{4(s + 2)}} + \frac{{s + 2}}{{4(s^2 + 4)}} = \frac{{ - 1}}{{4(s + 2)}} + \frac{s}{{4(s^2 + 4)}} + \frac{1}{{2(s^2 + 4)}}\).

I am willing to do this for because I think the topic ‘partial fractions’ is just one of many we should relegate to the scrap heap.

 

[Frogger888]

Thanks I am just having a case of bad algebra!!!