### Instruction: Find the domain of the function $\frac{x^4-4x^3+6x^2-4x+1}{x^2-4}$.### Response: To find the domain of a function, I need to look for values of x that would make the function undefined or invalid.
The only thing that could cause that in this function is the denominator, x^2-4, since it cannot be zero.
So I need to find the values of x that make x^2-4 = 0 and exclude them from the domain.
To do that, I can factor the denominator as (x-2)(x+2) and set each factor to zero.
This gives me x-2 = 0 and x+2 = 0, which imply x = 2 and x = -2.
These are the two values of x that I need to exclude from the domain, since they would make the function undefined.
The rest of the real numbers are valid for the domain, so I can write the domain as the set of all real numbers except 2 and -2.
Using interval notation, I can write this as (-infinity, -2) U (-2, 2) U (2, infinity), where U means union.