https://file.aiquickdraw.com/mathbot/file/1727056562969935tg094.jpg

The expression to simplify is:

\[
\frac{\frac{w^2 - x^2}{wx}}{\frac{w - x}{x}}
\]

### Step-by-Step Solution:

1. **Simplify the division of fractions**:
   When dividing two fractions, you multiply the first by the reciprocal of the second:
   \[
   \frac{\frac{w^2 - x^2}{wx}}{\frac{w - x}{x}} = \frac{w^2 - x^2}{wx} \times \frac{x}{w - x}
   \]

2. **Factor the difference of squares**:
   Recall the identity \(a^2 - b^2 = (a - b)(a + b)\). Applying this to \(w^2 - x^2\):
   \[
   w^2 - x^2 = (w - x)(w + x)
   \]
   So the expression becomes:
   \[
   \frac{(w - x)(w + x)}{wx} \times \frac{x}{w - x}
   \]

3. **Cancel out common terms**:
   The factor \(w - x\) appears in both the numerator and denominator, so it can be cancelled out:
   \[
   \frac{(w + x)}{w}
   \]

Thus, the simplified expression is:

\[
w + x
\]

Let me know if you need any further details or clarifications.

### Related Questions:
1. How would you handle this expression if \( w = x \)?
2. What is the result if both \( w \) and \( x \) are negative?
3. How does the difference of squares factoring apply in more complex algebraic expressions?
4. Can you extend this process to handle three variables like \(w^3 - x^3\)?
5. How would you simplify the original expression if \(x\) were in terms of another variable, say \(y\)?

### Tip:
Always look for factoring opportunities (like the difference of squares) when simplifying expressions!

Simplify the expression: (w² - x²) / wx ÷ (w - x) / x

Simplify the rational expression involving division of fractions and factoring the difference of squares. This solution breaks down the steps of simplifying (w² - x²) / wx ÷ (w - x) / x, ideal for high school algebra students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation