# Impulse response of a system in z domain

The question 3-23 in the "Discrete-Time Signal Processing - Second Edition" is:

and the solution is:

I cannot understand the solution. In the second row of the answer when I multiply (-4) with this denominator:

and then add the result to: it gives a result different from the numerator of the first row. This multiplication must be equal to

Which is not. Is this solution true? If yes, can anyone help me to understand if?

$$H(z) = -4 + \frac{ 5 + \frac{7}{2} z^{-1} }{1 - \frac{3}{4}z^{-1} + \frac{1}{8} z^{-1} }$$
$$H(z) = -4 + \frac{ 5 - 3 z^{-1} }{1 - \frac{3}{4}z^{-1} + \frac{1}{8} z^{-1} } .$$