Z transform getting different answer for transform of rational function

Why am i getting different answers and which one is correct??

In this also

Your first line is wrong. The partial fraction expansion of $$X(z)$$ should be :

$$X(z) = \frac{ z (2z-\frac{5}{6})}{ (z-\frac{1}{2})(z-\frac{1}{3})} = 2 + \frac{ \frac{1}{2} }{z - \frac{1}{2}} + \frac{ \frac{1}{3}}{z - \frac{1}{3}}$$

Then they should yield the same inverse (causal) transform as:

$$x[n] = 2\delta[n] + (1/2)^{n} u[n-1] + (1/3)^{n} u[n-1]$$

which is identical to : $$x[n] = (1/2)^n u[n] + (1/3)^n u[n]$$

as obtained by the second method.

• Ok got it but what about second question? Feb 29 '20 at 21:01
• your second question is allright. You should see that $$3^n u[n] - 2^n u[n] = 3^n u[n-1] - 2^n u[n-1]$$ for all $n$. Mar 1 '20 at 9:15