Fraction Addition with variables
Hi, Its been a while since I had to do work with fractions and as such I became extremely rusty.
The original equation is: x(n) = 2Q(n-2) + 3u(n-3)
Read Q as delta which denotes a impulse function and u(n) is the step sequence.
I found the Z-transform of that which is:
X(z) = 2*z^(-2)/1+(3*z^(-3))/(1 - z^(-1))
Working that out to find common denominator and adding the two parts:
(2*z^-2)*(1 - z^(-1))/(1 - z^(-1))
(2*z^(-2) - 2*z^(-3))/(1 - z^(-1)) + (3*z^(-3))/(1 - z^(-1))
2*z^(-2) + 3*z^(-3)/(1 - z^(-1)) %this is where I am stuck
I am aware that the answer is:
My Questions is How do I get from 2*z^(-2) + 3*z^(-3)/(1 - z^(-1)) to the answer.
I realize this much be quite simple but for some reason I am stuck. I look forward to laughing my self silly once this is answered or I figure it out.
Thanks In Advance