The expression you provided is:

\[
\frac{1}{1 - \left(1 - \frac{1}{x}\right)}
\]

First, simplify the expression inside the parentheses:

\[
1 - \frac{1}{x} = \frac{x - 1}{x}
\]

So the expression becomes:

\[
\frac{1}{1 - \frac{x - 1}{x}}
\]

Now, to simplify the denominator, combine the fractions:

\[
1 - \frac{x - 1}{x} = \frac{x}{x} - \frac{x - 1}{x} = \frac{x - (x - 1)}{x} = \frac{1}{x}
\]

So the entire expression simplifies to:

\[
\frac{1}{\frac{1}{x}} = x
\]

Thus, the simplified expression is:

\[
x
\]

Would you like more details or have any questions?

Here are some related questions you might find useful:
1. How would you simplify \(\frac{1}{1 + \left(1 - \frac{1}{x}\right)}\)?
2. What is the value of the expression when \(x = 2\)?
3. How do you simplify the expression \(\frac{1}{1 - \left(\frac{1}{x + 1}\right)}\)?
4. What happens if you replace \(x\) with \(\frac{1}{y}\) in the expression?
5. How would you graph the function \(f(x) = \frac{1}{1 - \left(1 - \frac{1}{x}\right)}\)?

**Tip:** When simplifying complex fractions, always look to combine terms in the denominator or numerator, then simplify step by step.

Learn how to simplify the fraction 1/(1 - (1 - 1/x)) step-by-step with detailed explanations. This problem covers fraction simplification in algebra, focusing on combining fractions and simplifying complex expressions. Suitable for students in Grades 9-12.

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