1. **State the problem:** Simplify or analyze the expression $$x^2 - 1 + x \mid 2 - x$$. 2. **Interpretation:** The vertical bar \mid can mean different things depending on context: it might indicate absolute value, divisibility, or a piecewise function separator. Since the expression is algebraic, we consider it as a piecewise function or division. 3. **If it is a piecewise function:** - For example, if the expression means $$f(x) = \begin{cases} x^2 - 1 + x & \text{if } x \geq 2 \\ 2 - x & \text{if } x < 2 \end{cases}$$ 4. **Simplify each piece:** - $$x^2 - 1 + x = x^2 + x - 1$$ - $$2 - x$$ remains as is. 5. **Summary:** The function is $$f(x) = \begin{cases} x^2 + x - 1 & \text{if } x \geq 2 \\ 2 - x & \text{if } x < 2 \end{cases}$$ 6. **Explanation:** This means for inputs greater or equal to 2, use the quadratic expression, and for inputs less than 2, use the linear expression. 7. **No further simplification is possible without more context.**