Final answer:
The proof that (b - a) / (a - b) < 0 is valid because a^3 < 0 implies a is negative, and factoring the expression results in -1, which is indeed less than 0.
Step-by-step explanation:
The student has presented a mathematical statement, Given a^3 < 0, prove b - a / a - b < 0. To evaluate this statement and prove the inequality, let's begin with the given information that a^3 < 0. This tells us that 'a' is a negative number because the cube of a positive number or zero cannot be less than zero.
The expression (b - a) / (a - b) can be simplified by factoring out a negative sign from the denominator, which gives us:
- (b - a) / (a - b) = (b - a) / (-(b - a))
- (b - a) / (a - b) = -1
Since -1 is less than 0, the given proof is valid. Hence, the correct answer is option B.