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so i know the denominator factors into s(s+3)(s+2)
good what is next ?
i have to split it up in 3 different fractions?
A, B, and C?
so ill have A/s + B/(s+3) + C/(s+2) ?
so this is where i get mixed up so hold on lol
so then i set A+B+C=5(1+s)?
or cross multiply first?
now you should multiply both sides by s(s+3)(s+2)
we gotta get common denominator right
how can A+b +c equal that otherwise
so like A (s(s+3)(s+2))?
A(s(s+3)(s+2))/s + B(s(s+3)(s+2))/(s+3) + C(s(s+3)(s+2))/(s+2) = 5(1+s)
this is how it looks when you multiply both sides by the denominator
okay yes thats what ive got!
fix your factoring first
dan ur confusing me
@dan815 is right by the way s(s^2+6s+5) = s(s+5)(s+1)
so A/s + B/(s+5) ?
thanks Dan that was my fault i was looking at the wrong problem when i factored the denominator!
so now cross multiply?
yes now multiply both sides by s(s+5) (the denominator)
cross multiply what?
the split fractions
you must get common denominator now so you can solve for a and b
5/[s(s+5)] = A/s + B/(s+5)
multiply both sides by s(s+5) ..
you get common denominator so you can equate the numerators and solve for a and b
we can extract 2 system of equations in this case from the numerator conditions one for the coefficient of s and the constant
after you solve for a and b you can write your a/s + b/s+5 function
this is pretty much how all your examplse will go
im sure your next question will involve some quadratic for the partial fractions we do the same thing, you split the numerators into some number of equations and solve some number of unknowns