Question

Determine the value of the co-efficient "B"
F(s)=7s^2+4s+2/(s+1)(s^2+s+5)=(A/s+1)+(Bs+C/s^2+s+5

Answer 1

no one seems to want to do this because it is a pain

Answer 2

you have to write
\[A(x^2+x+5)+(Bx+C)(x+1)=7x^2+4x+2\]
then multiply out. then equate like coefficients. then find them

Answer 3

you get \[Ax^2+Ax+5A+Bx^2+Bx+Cx+C=7x^2+4x+2\]

Answer 4

giving 3 equations
\[A+B=7\]
\[A+B+C=4\]
\[5A+C=2\]

Answer 5

i guess we can subtract the first from the second and get C = -3

Answer 6

replacing C by -3 in the third gives
\[5A-3=2\] so A=1
and finally replacing A by 1 equation 1 gives B = 6

what a pita

Answer 7

Thank you , you are the MASTER !!!

Answer 8

yes now i am a master. graduated from superhero

Answer 9

now you can explain these fourier series to me