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Math Help - Fraction Addition with variables

  1. #1
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    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.

    Thanks In Advance
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  2. #2
    MHF Contributor
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    Quote Originally Posted by StuckOnSimpleThings View Post
    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
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