Final answer:
To find x³ - 1/x³, you would typically expand (x - 1/x)³ and simplify. However, without the value of x - 1/x, it's not possible to select from the given answer choices A-D.
Step-by-step explanation:
The student has asked how to find x³ - 1/x³ given that x - 1/x is known. This is a problem that involves the operation of cubing an expression and understanding the rules of exponents. To solve for x³ - 1/x³, we will utilize the fact that (x - 1/x)³ equals x³ - 3x(x(1/x)) + 3(x(1/x))x - 1/x³, which simplifies to x³ - 3x + 3 - 1/x³. As we can see, +3 and -3 cancel each other out, leaving us with x³ - 1/x³. However, since we don't have the actual values to plug into x - 1/x, we cannot simplify further to one of the answer choices provided (A-D). Without additional information on the value of x, we cannot determine the exact form of x³ - 1/x³ from the given options.