%2F(x-1).jpeg "(1-x)/(x-1)")
The Expression (1-x)/(x-1)
The expression (1-x)/(x-1) might seem simple at first glance, but it holds a subtle mathematical twist. Let's explore its properties and implications.
Simplifying the Expression
At first glance, it might appear we can simply cancel out the (x-1) terms in the numerator and denominator, resulting in -1. However, this is incorrect. The reason lies in the order of operations.
The expression (1-x) is not the same as (x-1). They are opposites. This is crucial to understand when dealing with fractions.
The Correct Approach
To simplify (1-x)/(x-1), we can factor out a -1 from the numerator:
(1-x) = -1(x-1)
Now, we can rewrite the expression as:
(-1(x-1))/(x-1)
We can then cancel out the (x-1) terms, leaving us with -1.
Implications and Caveats
While the simplified result is -1, it's crucial to remember the caveat: this simplification only holds true when x ≠ 1. Why? Because if x = 1, the denominator becomes zero, resulting in an undefined expression.
In Summary
The expression (1-x)/(x-1) simplifies to -1, but only for values of x ≠ 1. Understanding this distinction is crucial for accurate mathematical analysis.