I have the following equation:
$\frac{Z-1}{{Z^2}-2Z+6}$
I tried to apply difference equation on it:
$y_{n+2}-5y_{n-1}-6y_n = x_{n+1}-x_n$
I need to find equation expressed as $y_n$
I have the answer (At the end of the chapter) to be: $y_n = 5y_{n-1}-6y_{n-2}+x_{n-1}-x_{n-2}$
Can somone please tell me how did in this case the second equation expressd as $y_n$ ? I cant figure it out!