Evaluate f(x) X2-25÷x-5

April 30, 2026Mathematics

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Answer

f(x) = x + 5, \text{ for } x \neq 5

2 steps

The function is given by $f(x) = \frac{x^2 - 25}{x - 5}$ .

Factor the numerator.
The numerator is a difference of squares, $x^2 - 25 = (x - 5)(x + 5)$ .
$f(x) = \frac{(x - 5)(x + 5)}{x - 5}$
Cancel out the common factor $(x - 5)$ from the numerator and denominator, assuming $x \neq 5$ .
$f(x) = x + 5, \quad \text{for } x \neq 5$
The function $f(x)$ simplifies to $x + 5$ for all values of $x$ except $x = 5$ . At $x = 5$ , the original function is undefined.

The simplified expression for $f(x)$ is $x + 5$ .

f(x) = x + 5, for x \neq 5

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