Final answer:
The expression (8y) / (y - 2) - (16) / (y - 2) simplifies to 8, provided that y is not equal to 2. This is because the terms (y - 2) cancel out in the numerator and denominator after subtraction and simplification.
Step-by-step explanation:
To answer the student's question on how to subtract (8y) / (y - 2) minus (16) / (y - 2), we start by recognizing that the denominators are the same. This allows us to combine the numerators directly over a single denominator. So we compute:
(8y) / (y - 2) - (16) / (y - 2) = (8y - 16) / (y - 2)
Now, we can simplify the numerator:
(8y - 16) / (y - 2) = 8(y - 2) / (y - 2)
Since the (y - 2) terms are the same in the numerator and the denominator, they cancel each other out, assuming y ≠ 2 (because we cannot divide by zero).
Therefore, the final result is simply:
8, as long as y ≠ 2.