Question

$( + x)( + y) = + xy = + xy \div ( + y) = + x$
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Answer 1

Answer:

Probably the best way to solve this problem is plug-in method. Though there are two properties worth to remember:

1. Always true: , note that "=" sign holds for (or simply when and have the same sign);

2. Always true: , note that "=" sign holds for (so when and have the same sign) and (simultaneously). (Our case)

So, the question basically asks whether we can exclude "=" scenario from the second property.

(1) y < x --> we can not determine the signs of and . Not sufficient.

(2) xy < 0 --> "=" scenario is excluded from the second property, thus . Sufficient.