%2F(x-3).jpeg "(x^2-9)/(x-3)")
Simplifying the Expression (x^2 - 9) / (x - 3)
The expression (x^2 - 9) / (x - 3) represents a rational function, which is a fraction where both the numerator and denominator are polynomials. We can simplify this expression by factoring the numerator and then canceling common factors.
Factoring the Numerator
The numerator, x^2 - 9, is a difference of squares. We can factor it as follows:
x^2 - 9 = (x + 3)(x - 3)
Simplifying the Expression
Now we can rewrite the original expression:
(x^2 - 9) / (x - 3) = [(x + 3)(x - 3)] / (x - 3)
Since (x - 3) appears in both the numerator and denominator, we can cancel them out:
[(x + 3)(x - 3)] / (x - 3) = x + 3
Important Note
While we have simplified the expression, it's crucial to remember that the original expression is undefined when x = 3. This is because the denominator becomes zero, leading to an undefined result.
Therefore, the simplified expression, x + 3, is equivalent to the original expression (x^2 - 9) / (x - 3) for all values of x except x = 3.