How me in more detail. I am confuse with the coeffictients like how he set s=-2

Question

How me in more detail. I am confuse with the coeffictients like how he set s=-2 just show me coefficitents part in detail i am trying to understand it

Next step is to use expand the 2 fractions, ignoring for the moment the exponential: 40s + 160/s2 + 4s +40 = A s+2/(a+2 +6 +6 +b 6/(s+2)2 +62 40s + 160= A(s + 2) + 6B setting s = -2 80 = 6B or B = 40/3 looking at the coefficients of s on each side gives A = 40 setting s = 0 E -1 looking at the coefficients ofs2 on each side gives 0 = C + E C = -1 setting s = -2 gives 40 = -12D+36E D = 3

Explanation / Answer

after u get first step and now u can take the LCM u get A(s+2)+6B

now u get 40s+160 eqal to A(s+2)+6B

so now to get B u need to eliminate A so u can do it by s= -2

so u get 40*(-2) + 160 = 6B

now equate the coeeficients on both sides of s

40s = A s

so A = 40

now ater words u have this E which is obtained by equating the coeeicients of s^2

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