%2F(x-2).jpeg "(x^2-4)/(x-2)")
Simplifying the Expression: (x^2 - 4) / (x - 2)
The expression (x^2 - 4) / (x - 2) can be simplified by factoring the numerator and then cancelling common factors. Here's how:
Factoring the Numerator
The numerator (x^2 - 4) is a difference of squares. We can factor it as:
(x^2 - 4) = (x + 2)(x - 2)
Simplifying the Expression
Now, we can substitute the factored numerator back into the original expression:
(x^2 - 4) / (x - 2) = [(x + 2)(x - 2)] / (x - 2)
Since (x - 2) appears in both the numerator and denominator, we can cancel them out:
[(x + 2)(x - 2)] / (x - 2) = x + 2
Restrictions
It's important to note that the original expression is undefined when x = 2. This is because the denominator becomes zero. However, the simplified expression x + 2 is defined for all values of x.
Therefore, the simplified form of (x^2 - 4) / (x - 2) is x + 2, but it is valid only for x ≠ 2.