Question
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Answer
The expression simplifies to -1.
Solution
Calculate or simplify the expression \( (x-y)/(y-x) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(x-y\right)}{\left(y-x\right)}\)
- step1: Remove the parentheses:
\(\frac{x-y}{y-x}\)
- step2: Calculate:
\(\frac{x-y}{-\left(x-y\right)}\)
- step3: Reduce the fraction:
\(-\frac{1}{1}\)
The simplified form of \( \frac{x-y}{y-x} \) is \( -1 \).
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Simplify this solution Beyond the Answer
Did you know that the expression \( \frac{x-y}{y-x} \) can be simplified into a much neater form? If you factor out -1 from the denominator, you'll find that it becomes \( \frac{x-y}{-(x-y)} \), which is simply \(-1\) as long as \(x \neq y\). This little trick highlights the beauty of algebraic manipulation! In the real world, this kind of transformation can be incredibly useful. For example, in economics, you might encounter rates of change that can be rearranged, allowing clearer insights into supply and demand dynamics. Understanding how to simplify expressions efficiently can lead to quicker calculations and better decision-making in various fields!
