Evaluate the limit:lim𝑥→2𝑥−2𝑥2−4=

To evaluate the limit of the function as x approaches 2, we first simplify the function. The function is given as (x - 2) / (x^2 - 4).

Step 1: Simplify the function The denominator (x^2 - 4) can be factored as (x - 2)(x + 2) using the difference of squares formula. So, the function becomes (x - 2) / [(x - 2)(x + 2)].

Step 2: Cancel out the common factors The (x - 2) in the numerator and denominator cancel out, leaving us with 1 / (x + 2).

Step 3: Substitute the limit Now, we substitute x = 2 into the simplified function, which gives us 1 / (2 + 2) = 1 / 4.

So, the limit of the function as x approaches 2 is 1/4.