(2) \( \frac{2}{x}-\frac{x}{x} \)

To combine the fractions in the expression \( \frac{2}{x}-\frac{x}{x} \), we first simplify the second fraction. Since \( \frac{x}{x} = 1 \), we can rewrite the expression as \( \frac{2}{x} - 1 \). Now, to combine these fractions into a single expression, we need a common denominator, which is \( x \). So, rewriting \(-1\) as \(-\frac{x}{x}\) gives us: \[ \frac{2}{x} - \frac{x}{x} = \frac{2 - x}{x} \] Hence, the expression simplifies to \( \frac{2 - x}{x} \). --- Simplifying fractions is not just about putting numbers together; it has roots in ancient mathematics where civil engineers used fractions to calculate areas and load distributions in constructions. Did you know that the ancient Egyptians had a method using unit fractions to perform calculations? They were quite the math wizards for their time! In practical terms, mastering fraction simplification is crucial in various fields like finance, engineering, and even cooking! One common mistake is forgetting to find a common denominator when subtracting or adding fractions, leading to incorrect results. Always double-check that the denominators match!