It looks like you're trying to simplify or solve the expression \(x^{n+1} - 2x^n + x^{n-1}\).

Let's break it down step by step:

1. **Identify common factors:**
Notice that each term has a factor of \(x^{n-1}\):
\[
x^{n+1} = x^{(n-1)+2} = x^{n-1} \cdot x^2
\]
\[
-2x^n = -2x^{(n-1)+1} = -2x^{n-1} \cdot x
\]
\[
x^{n-1} = x^{n-1}
\]

2. **Factor out \(x^{n-1}\):**
\[
x^{n+1} - 2x^n + x^{n-1} = x^{n-1}(x^2 - 2x + 1)
\]

3. **Simplify the quadratic expression inside the parentheses:**
The expression \(x^2 - 2x + 1\) can be recognized as a perfect square:
\[
x^2 - 2x + 1 = (x - 1)^2
\]

4. **Combine the results:**
\[
x^{n-1}(x^2 - 2x + 1) = x^{n-1}(x - 1)^2
\]

So, the simplified form of the given expression is:
\[
x^{n+1} - 2x^n + x^{n-1} = x^{n-1}(x - 1)^2
\]