### Instruction: Solve
\[\frac{x - 4}{(x - 2)^2} < 0.\]Enter your answer using interval notation.### Response: I want to find all the values of x that make this fraction negative.
A fraction is negative when the numerator and denominator have opposite signs, so I can split the problem into two cases: either x - 4 is negative and (x - 2)^2 is positive, or x - 4 is positive and (x - 2)^2 is negative.
The second case is impossible, because a square can never be negative.
So I can ignore it and focus on the first case.
To make x - 4 negative, x has to be less than 4.
To make (x - 2)^2 positive, x cannot be equal to 2, because then the denominator would be zero and the fraction would be undefined.
So the possible values of x are those that are less than 4 but not equal to 2.
In interval notation, this is (-∞, 2) ∪ (2, 4).