I was finding the domain of a multi variable function, and as a result I had to solve this inequality.
I was under the impression you could divide across an inequality sign without changing it's direction (and have it remain equal to what it was before), as long as what you were diving wasn't negtaive, but if you look at the two shades areas are different.
Is there a rule I'm forgetting? Thanks in advance
For $x>0$ we have $y<\frac{1}{x},$ while for $x<0$ we have $y>\frac{1}{x},$ which gives all points on the plane between branches of the hyperbola $xy=1$.