I have the following expression:

x(Z) = 16/15*(1/(1-(1/4)z^-1)) - 16/15*(1/(1-4*z^-1))

According to my understanding this should become:

x1(n) = 16/15*(1/4)^n * u(n) - 16/15*(4)^n * u(n)

But according to my source it is:

x2(n) = 16/15*(1/4)^n * u(n) + 16/15*(4)^n * u(-n-1)

Are the expressions equal, x1 = x2 ?

If they are, how can -1*u(n) = u(-n-1) ?

If not, why?

I used a^nu(n) <=z-transform=> 1/(1-az^-1)

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 $a^nu(n)\Longleftrightarrow \frac{1}{1-az^{-1}}$.