so i thought i knew about partial fractions, but apparently i don't. i have the answer to a partial fraction but i can't figure out how you get to that answer.
the value is $$ X(z) = Z*(Z+2)/(Z-1)^2 = 1 + 3z/(z-1)^2+1/(z-1) $$
Where does the "1" comes from? in the 1+ .......
Thanks
The numerator and denominator have the same degree, so the answer will have a constant term. More generally, for any polynomial $f(z)$, you can rewrite $$\frac{f(z)}{(z-1)^2} = g(z) + \frac{Az+B}{(z-1)^2}$$ where the degree of $g(z)$ will be $2$ less than the degree of $f$. This decomposition follows from polynomial long division.