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Z transform shifting in Wolfram|Alpha

Posted 24 days ago
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Hello I have a question about z transform. Please help me. I have this in wolfram:

enter image description here

in my book says that I can use the formula:

enter image description here

but, if I transform

enter image description here

if I apply the formula it would be (1 + 2 z))/(3 (1 + z + z^2)

but wolfram gives me instead:

enter image description here

Thank you, please help me.

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