The expression you've provided is:

\[
x^{-1} \cdot (2x - 1)
\]

This can be simplified as follows:

1. Recognize that \(x^{-1}\) is equivalent to \(\frac{1}{x}\).
   
   So the expression becomes:
   \[
   \frac{1}{x} \cdot (2x - 1)
   \]

2. Distribute \(\frac{1}{x}\) to each term inside the parentheses:
   \[
   \frac{1}{x} \cdot 2x - \frac{1}{x} \cdot 1
   \]

3. Simplify each term:
   - \(\frac{1}{x} \cdot 2x = 2\)
   - \(\frac{1}{x} \cdot 1 = \frac{1}{x}\)

   Therefore, the simplified expression is:
   \[
   2 - \frac{1}{x}
   \]

So, \(x^{-1} \cdot (2x - 1)\) simplifies to:

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

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How would you handle the expression if \(x = 0\)?
2. What happens to the expression as \(x\) approaches infinity?
3. Can this expression be integrated with respect to \(x\)?
4. How does the expression behave for negative values of \(x\)?
5. How would the expression change if we replaced \(x^{-1}\) with \(x^{-2}\)?

**Tip:** Remember that when simplifying expressions, distributing and combining like terms can often make the problem much easier to solve.

Learn how to simplify the expression x^-1 (2x - 1) with our detailed step-by-step solution. Understand the concept of simplification in algebra and how to distribute and combine terms. Suitable for high school students and anyone interested in algebraic simplification.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation