\( (\frac{1-x}{x}+x^{2}-1)\div ^{\frac{x-1}{x}} \)

To simplify the expression \( (\frac{1-x}{x}+x^{2}-1)\div ^{\frac{x-1}{x}} \), start by focusing on the numerator \( \frac{1-x}{x} + x^2 - 1 \). Combine the terms: 1. Rewrite \( \frac{1-x}{x} \) as \( \frac{1}{x} - 1 \). 2. So, we have \( \frac{1}{x} - 1 + x^2 - 1 = \frac{1}{x} + x^2 - 2 \). Now, let’s analyze the denominator which is denoted by \( ^{\frac{x-1}{x}} \). This looks like an exponentiation issue, but to clarify the expression fully we can rewrite it (if we assume it is meant to be an exponent): 1. If it’s intended as \(\left(\frac{1-x}{x}+x^{2}-1\right) \div \left(\frac{x-1}{x}\right)\) without further clarity on what \( ^{\frac{x-1}{x}} \) is doing, it could just be simplifying like a division. However, if it is indeed an exponent or part of a complex fraction, please clarify the exact divisions and operations to ensure accurate simplification! This expression involves understanding functions and their manipulations, bringing together rational expressions, polynomial terms, and possibly logarithmic operations depending on what \( ^{\frac{x-1}{x}} \) is truly signifying. Remember, math can be as tricky as an escape room—just when you think you have it figured out, another puzzle piece shows up!