Given two functions \(f(x) = x^2 - 4\) and \(g(x) = 2x - 4\), find the domain of the quotient function \(h(x) = \frac{f(x)}{g(x)}\).

Step 1 ：Step 1: Identify the domain of the individual functions. For \(f(x)\), the domain is all real numbers since \(f(x)\) is a polynomial. For \(g(x)\), the domain is also all real numbers since \(g(x)\) is a linear function. Therefore, the combined domain of \(f(x)\) and \(g(x)\) is all real numbers.

Step 2 ：Step 2: Identify any values that would make \(g(x)\) equal to zero since division by zero is undefined. Set \(g(x)\) equal to zero and solve for \(x\): \[2x - 4 = 0 \Rightarrow x = 2\]

Step 3 ：Step 3: Exclude the value \(x = 2\) from the combined domain of \(f(x)\) and \(g(x)\) since \(g(2)\) equals zero. Therefore, the domain of \(h(x)\) is all real numbers except \(x = 2\).