In the question, aren’t answers D and E equivalent, the only difference being the two terms are multiplied by negative 1?
D) \frac{1}{y} - \frac{1}{xy}\rightarrow \frac{x}{xy} - \frac{1}{xy} \rightarrow \boxed{\frac{x - 1}{xy}}
E) \frac{1}{xy} - \frac{1}{y} \rightarrow \frac{1}{xy} - \frac{x}{xy} \rightarrow \frac{1 - x}{xy}
To answer your question,
-1(1 - x) = x - 1, so yes, it is just multiplying by -1, but no, it does not meet the qualifications of the multiplicative identity property (a number multiplied by 1 is itself).
Perfect, this makes sense. Thank you!