I have the following expression:
$$X(z) = \frac{16}{15}\frac{1}{1-\frac14z^{-1}} - \frac{16}{15}\frac{1}{1-4z^{-1}}$$
According to my understanding this should become:
$$x(n) = \frac{16}{15}\left(\frac14\right)^n u(n) - \frac{16}{15} 4^n u(n)$$
But according to my source it is:
$$x(n) = \frac{16}{15}\left(\frac14\right)^n u(n) + \frac{16}{15} 4^n u(-n-1)$$
Are these expressions equal?
If they are, how can $-u(n) = u(-n-1)$ ?
If not, why?
I used $a^nu(n)\Longleftrightarrow \frac{1}{1-az^{-1}}$.