### 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 determine what values of x can be plugged into the function without causing any undefined expressions, such as division by zero or negative square roots.
The denominator of the function is x^2-4, which can be factored as (x-2)(x+2).
This means that the denominator will be zero when x is either 2 or -2.
Therefore, I cannot have x=2 or x=-2 in the domain of the function, because that would make the function undefined.
So, the domain of the function is all real numbers except 2 and -2.
I can write this domain using set notation as {x | x is a real number and x is not equal to 2 or -2}, or using interval notation as (-infinity, -2) union (-2, 2) union (2, infinity).