Find the range of the function $f(x)=\frac{x^2-4}{x-2}$ for $x\ne 2$.

Step-by-step solution

1. Factor the numerator: $x^2-4=(x-2)(x+2)$.
2. Cancel the common factor $x-2$ for $x\ne 2$ to obtain $f(x)=x+2$.
3. As $x$ runs over $\mathbb{R}\setminus \{2\}$, $x+2$ runs over $\mathbb{R}\setminus \{4\}$.
4. Thus the range is $\mathbb{R}\setminus \{4\}$.

Concept tested: Range of rational function with hole

Published 18 September 2026 · How this solution was prepared and checked