To simplify the expression \(\frac{\left( \frac{1}{2} + x \right) - \frac{1}{2}}{x}\):

1. First, notice that the \(\frac{1}{2}\) terms in the numerator cancel out:
   \[
   \frac{1}{2} + x - \frac{1}{2} = x
   \]

2. Now the expression simplifies to:
   \[
   \frac{x}{x}
   \]

3. Since \(\frac{x}{x} = 1\) (as long as \(x \neq 0\)):

   The simplified expression is \(1\).

### Final Answer:
\[
1 \quad \text{(for} \, x \neq 0\text{)}
\]

Would you like any further details on this or another question?

Here are five related questions for further exploration:
1. What is the domain of this expression?
2. How does this result change if \(x = 0\)?
3. Can this expression be approached using limits as \(x\) approaches 0?
4. What happens if we add additional terms like \(\frac{1}{2}x^2\) to the numerator?
5. How would this problem change if the denominator was \(x^2\)?

**Tip**: Always check if terms can cancel out before attempting more complex simplifications!

Understand how to simplify the rational expression ((1/2 + x) - 1/2) / x by canceling like terms and applying basic fraction operations. This step-by-step solution is ideal for students in Grades 6-8, helping them learn essential algebraic concepts such as simplification and the cancellation property.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation