Let $f\left(x\right)=\frac{x^2-4}{x-2}$. <IMAGE>
Make a conjecture about the value of ${\displaystyle\lim_{x\to2}\frac{x^2-4}{x-2}}$.

Verified step by step guidance

1. First, recognize that the expression $\frac{x^2-4}{x-2}$ is undefined at $x=2$ because it results in division by zero. Therefore, we need to simplify the expression to evaluate the limit.
2. Notice that the numerator $x^2-4$ can be factored as a difference of squares: $x^2-4=(x-2)(x+2)$.
3. Substitute the factored form into the original expression: $\frac{(x-2)(x+2)}{x-2}$.
4. Cancel the common factor $(x-2)$ in the numerator and the denominator, which simplifies the expression to $x+2$, provided $x\ne 2$.
5. Now, evaluate the limit of the simplified expression as $x\to 2$: $\underset{x\to 2}{lim}(x+2)$. This can be directly computed by substituting $x=2$ into the expression, leading to the conjecture about the limit.