Answer:
To find the domain of the function f(x) = (x-7)(x-1)/(x+3)(x-1), we need to consider the values of x that make the denominator zero since division by zero is undefined.
In this case, the denominator (x+3)(x-1) is zero when x = -3 and x = 1. Therefore, we need to exclude these values from the domain.
So, the domain of f(x) is all real numbers except x = -3 and x = 1.
In interval notation, we can write the domain as (-∞, -3) U (-3, 1) U (1, ∞).