which is the correct partial fraction for 1/z^2(z+1)
A. (Ax+B)/z^2+C/(z+1)
B. A/z+B/Z^2+C/(z+1)

Question

which is the correct partial fraction for 1/z^2(z+1) 
A.  (Ax+B)/z^2+C/(z+1)  
B. A/z+B/Z^2+C/(z+1)

bradely · Answer

B is correct

anonymous · Answer

why is A not correct it is z^2

zepdrix · Answer

$$\Large\rm \frac{1}{z^2(z+1)}=\frac{Az+B}{z^2}+\frac{C}{z+1}$$Neither option is incorrect. You can think of the z^2 as a `repeated linear factor` in which case you would break it down like in option B.
Or you can think of it as a `quadratic` in which case it would break down with a linear factor on top as in option A.

anonymous · Answer

ohh thanks .. i was also confused about this ... i felt both are correct too.

zepdrix · Answer

Option B is a little nicer to work with I think. Maybe that's just preference though :)