Here's the question you clicked on:
shivamsinha
if s^2(a+b)+s(b+c)+a+c=1 then hw is a+b=0,c+b=0, a+c=1
this is partial fractions?
well in any event, you are trying to set the coefficients on each side equal on the right, the coefficient of the s^2 term must be zero, since there is no s^2 term hence the coefficient for s^2 on the left must also be zero
similarly with the s term the only term that is on the right is the constant term, which is 1 hence the constant term on the left (the term that does not have an s in it) must equal 1 a+c=1