Inspect using long division and determine the inverse z transform of 
X(z) = z + 1
          Z2 – 3z + 2

To find the inverse Z-transform of \( X(z) = \frac{z + 1}{z^2 - 3z + 2} \) using long division, we will perform the division and identify the resulting sequence in the time domain.

### Step 1: Perform Long Division

Given:
\[
X(z) = \frac{z + 1}{z^2 - 3z + 2}
\]

First, let's factor the denominator if possible:
\[
z^2 - 3z + 2 = (z - 1)(z - 2)
\]

Now, perform the long division:

1. Divide the highest degree term in the numerator by the highest degree term in the denominator:
   \[
   \frac{z}{z^2} = \frac{1}{z}
   \]
   But we need terms in decreasing powers of \( z \). This step suggests we'll rewrite it as \( 0 \) for this stage of division and continue for lower degree terms.

Since \( \frac{z}{z^

Inspect using long division and determine the inverse Z-transform of X(z) = (z + 1) / (z^2 - 3z + 2).

Learn how to find the inverse Z-transform of X(z) = (z + 1) / (z^2 - 3z + 2) using long division and partial fraction decomposition. The step-by-step solution demonstrates key mathematical techniques like polynomial division and the inverse Z-transform. Suitable for undergraduate students studying engineering or applied mathematics.

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