Explanation

This question could obviously involve a lot of algebra, but we can analyze it by cases. Namely, we can examine a case of allowed variables of x and y. To make things as simple as possible, maybe we can have y=2, so that . That doesn't yield great values for x. Trying it the other way, if were 8 and 2, so that , then and . Looking at the answer choices, working with directly should be manageable. So we have an allowed case: . Let's see how the answer choices hold up in this case:

. That's , which is true. So (A) is maybe equivalent to our starting equation.

. That gives , so (B) also may be equivalent to our starting equation.

. That gives , so (C) also may be equivalent to our starting equation.

. This is not true. So this equation is NOT equivalent to our starting equation. We can check (E) to be sure.

. That's true, so this equation may be equivalent to our starting equation.

We looked at a case that was allowed by our original equation, and it was allowed by all of the answer choices except (D). Therefore (D) must be the equation that is not equivalent to the original.

The correct answer is (D).