# Question: (x-y)/xy

## Comment on (x-y)/xy

### But by dividing the equation

But by dividing the equation by 2x+1, are we not ruling out the case that (2x+1) could equal 0 i.e. x=-1/2 ### Great question!!!

Great question!!!
It turns out that the original equation, (x - y)/xy = 2, already rules out the possibility that x = -1/2

To see why this is, let's replace x with -1/2 to see what happens.

We get: (-1/2 - y)/(-1/2)(y) = 2

Multiply both sides by -y/2 to get: -1/2 - y = -y

Add y to both sides to get: -1/2 = 0

So, there is no valid solution in which x = -1/2 (i.e., 2x+1 = 0)

### Brent,

Brent,

I love your videos! I had a quick question - I incorrectly applied arithmetic here and I can't figure out why it is wrong:

1... (x-y)/xy = 2
2... x/xy - y/xy = 2
3... 1/y - 1/x = 2
4... y - x = 1/2
5... y = x + 1/2

Thanks!
D ### Your solution is solid up

Your solution is solid up until line #4.

If we have a SINGLE fraction on each side, then we can use the approach you used.
That is, if x/y = a/b, then we can also say that y/x = b/a (provided a and x don't equal zero)
For example, if 3/6 = 1/2, we can also say that 6/3 = 2/1

However, if we have TWO fractions on one side, then the approach falls apart.

For example, we know that 1/2 - 1/4 = 1/4
However, we cannot then conclude that 2/1 - 4/1 = 4/1
Likewise, if 1/y - 1/x = 2, we cannot then conclude that y/1 - x/1 = 1/2 (as you have done in line #4)

Does that help?

Cheers,
Brent

### Yes! Thanks for the quick

Yes! Thanks for the quick response.