1. ## 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:

(2*z+1)/((z-1)*z^(2))

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.

2. Originally Posted by StuckOnSimpleThings
2*z^(-2) + 3*z^(-3)/(1 - z^(-1))
That should be: 2*z^(-2) + z^(-3)/(1 - z^(-1))
(I'll let you have the pleasure of going back over your work to this point!)

Now, to get to the given answer:

You probably just forgot this rule: a^(-b) = 1 / a^b
Keeping that in mind:
2*z^(-2) + z^(-3)/(1 - z^(-1))

= (2 / z^2 + 1 / z^3) / (1 - 1 / z)

= [(2*z + 1) / z^3] / [(z - 1) / z]

Now you can have the pleasure of wrapping that up