Final answer:
The question likely pertains to finding the domain and simplifying the rational function f(x) = (x² - x) / (-4x + 16), where the domain excludes x = 4 and the function simplifies to -x/4.
Step-by-step explanation:
The student is working with various forms of quadratic equations and operations on rational functions in the realm of algebra. In the case of the provided function f(x) = (x² - x) / (-4x + 16), a question could involve finding the domain, simplifying the function, or possibly solving for x when the function is set equal to another value.
An example question could be: What is the domain of the function f(x) = (x² - x) / (-4x + 16) and how can this function be simplified? To solve for the domain, we need to identify the values of x for which the function is defined, which means finding where the denominator isn't zero. Simplifying the function involves factoring the numerator and denominator and cancelling out common factors if possible.
Working through these steps, we'd find that the denominator -4x + 16 can be factored to -4(x - 4). The numerator x² - x can be factored to x(x - 1). Cancelling the factor x - 4 from both the numerator and denominator (provided that x ≠ 4 to avoid division by zero), gives a simplified function of -x/4 for x ≠ 4. Thus, the domain of the original function is all real numbers except 4.