How does the following come about? I'm completely lost. Can anyone help me fill in the steps in between?

$$ \frac{s+2}{s(s+1)} = \frac{2}{s} - \frac{1}{s+1} $$

I figured that $$ \frac{s+2}{s(s+1)} = \frac{s}{s(s+1)} + \frac{2}{s(s+1)} = \frac{1}{s+1} + (\text{not sure}) $$

  • 1
    $\begingroup$ Thanks @lab bhattacharjee ! I should've known to to that since this is one of the last steps of a differential equations problem. Thanks again! $\endgroup$ – user12279 Nov 19 '13 at 4:46


Using Partial Fraction Decomposition,

$$ \frac{s+2}{s(s+1)}=\frac As+\frac B{s+1}$$

$$ \implies s+2=A(s+1)+Bs$$ $$ \implies s+2=s(A+B)+A$$

$$ \text{Now, Compare the constants & the coefficients of $s$}$$


Well, you can note that $$s+2=(s+1)+1=(s+1)+(s+1-s)=2(s+1)-s,$$ so that $$\frac{s+2}{s(s+1)}=\frac{2(s+1)-s}{s(s+1)}=\frac{2(s+1)}{s(s+1)}-\frac s{s(s+1)}=\frac2s-\frac1{s+1}.$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.