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Hello again,
(See attachment for clearer math expressions)
I tried the "FORM 1" idea to see how it would work.
This was with the problem:
(5*(2*s^3-433*s^2+44000*s-4330000))/(4*(s^2+10000)*(s^2+100*s+1250))
This was interesting because this problem already has the two factors in the denominator written out, the two second degree factors in the denominator. That means our assumed solution would look like:
(A*s+B)/(s^2+10000)+(C*s+D)/(s^2+100*s+1250)
Now equating the first expression above to the second expression above, we end up with:
10*s^3-2165*s^2+220000*s-21650000=4*s^2*D+40000*D+4*s^3*C+40000*s*C+4*s^2*B+400*s*B+
5000*B+4*s^3*A+400*s^2*A+5000*s*A
Solving that for A,B,C, and D, and forming the new expression, we get:
(1802*s-254245)/(452*(s^2+100*s+1250))-(168*s-19200)/(113*(s^2+10000))
and now we see this problem has been broken down into two separate parts which can be solved separately if needed. It is interesting that this solution is a partial fraction expansion, it's just not in its most elemental form. In some cases this may be enough.
Of course we check the new expression against the original. It does come out to be identical.
(See attachment for clearer math expressions)
I tried the "FORM 1" idea to see how it would work.
This was with the problem:
(5*(2*s^3-433*s^2+44000*s-4330000))/(4*(s^2+10000)*(s^2+100*s+1250))
This was interesting because this problem already has the two factors in the denominator written out, the two second degree factors in the denominator. That means our assumed solution would look like:
(A*s+B)/(s^2+10000)+(C*s+D)/(s^2+100*s+1250)
Now equating the first expression above to the second expression above, we end up with:
10*s^3-2165*s^2+220000*s-21650000=4*s^2*D+40000*D+4*s^3*C+40000*s*C+4*s^2*B+400*s*B+
5000*B+4*s^3*A+400*s^2*A+5000*s*A
Solving that for A,B,C, and D, and forming the new expression, we get:
(1802*s-254245)/(452*(s^2+100*s+1250))-(168*s-19200)/(113*(s^2+10000))
and now we see this problem has been broken down into two separate parts which can be solved separately if needed. It is interesting that this solution is a partial fraction expansion, it's just not in its most elemental form. In some cases this may be enough.
Of course we check the new expression against the original. It does come out to be identical.
Last edited:
