I assume that the question was:
IS (x-y)/(x+y) > 1?
(Please clearly post the question, makes our lives easier when trying to help.)
You made a classic inequality mistake. We CANNOT simply "move over" variables if we don't know the signs of what we're "moving".
Let's examine what you did:
(x-y)/(x+y) > 1
->x-y > x + y
to get to this inequality, you must have multiplied both sides by (x+y). However, we have to remember that if we ever multiply or divide both sides of an inequality by a negative, the inequality flips directions.
So, we end up with TWO solutions:
If (x+y) is positive, then we get:
Is x-y > x+y?
But, if (x+y) is negative we get:
Is x-y < x+y?
And, of course, each of those simplifies to different questions.
So, when going through the statements, we really need to pay attention to the signs.
Back to our originally scheduled program:
Is (x-y)/(x+y) > 1
(1) x > 0
We know nothing about y, so just knowing that x is positive doesn't allow us to answer the question. We could pick numbers to make the left side either positive or negative.
(2) y < 0
We know nothing about x, so just knowing that y is negative doesn't allow us to answer the question. We could pick numbers to make the left side either positive or negative.
Together:
If we know that x is positive and y is negative, we know that the top of our fraction is:
(+) - (-) = +
and the bottom of our fraction is:
(+) + (-) = ?? (depends on the actual numbers).
So, even together we have no clue if the left side is positive or negative: choose (e).
