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