If X does not = Y, but X/Y + X = Y/X + X, what does 1/X + 1/Y equal?

Question

X/Y + X/1 = Y/X + X/1
X/1 cancels out

X/Y = Y/X
X^2 = Y^2
+/-X = +/-Y
In effect, if X != Y, then:
X = -Y or -X = Y

So,
1/X + 1/Y = 0

sorrry, but I made a typo.
x/y + x = Y/x + Y.