(x+y)/(x-y)*(x-y)/(x+y)

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So this is an equation I found with interesting properties. Pretty much x+y=z and x-y=z are linear equations of 2 equations 2 unknowns. If you solve for this equation you get x=z and y=0. Now I haven't got a chart for x-y=z, Google shows the x+y=z chart but not the other one, if you have it please show me.

Now for z=(x+y)/(x-y) it generates an interesting chart in google, same goes for z=(x-y)/(x+y). I'm not sure if they are off by 180 degrees or simply upside down. Now when you multiple the two together you get z^2=1 which is z=1 not z=0. This seems to be an interesting property and if someone can give me an explanation on this it would be cool.

To sum up:

1. Get me a chart for x-y=z

2. z=(x+y)/(x-y) and z=(x-y)/(x+y) looks interesting, when you multiply them together you get z=1, why is that and what does that mean?

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Isn't (x+y)/(x-y)*(x-y)/(x+y) equal to LaTeX:

$\frac{x+y}{x-y}*\frac{x-y}{x+y}$

??

Maybe some parenthesis missing somewhere?

Which is equal to:

$\frac{x+y}{x+y}*\frac{x-y}{x-y}$

$1*1$

$1$

(as long as no division by 0)

f.e. if I make OpenOffice SpreadSheet

with A1=1000 B1=500

and C1=(A1+B1)/(A1-B1)*(A1-B1)/(A1+B1)

Result is 1.

If I make A1=B1=1000 f.e.

OpenOffice complains there is division by 0.

Now for z=(x+y)/(x-y) it generates an interesting chart in google, same goes for z=(x-y)/(x+y). I'm not sure if they are off by 180 degrees or simply upside down.

They will be z'=1/z

or z'=z-1

Edited by Sensei
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They will be z'=1/z

or z'=z-1

Hi Sensei, can you clarify on this one? Did you take the derivative or something? I know my equation becomes z=1, I'm just not sure why that is the case. If you take a look at z=(x+y)/(x-y) it looks like a spiral, so how come a spiral multiplies by another spiral becomes z=1? Also get me a chart on x-y=z, many thanks

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I know my equation becomes z=1, I'm just not sure why that is the case. If you take a look at z=(x+y)/(x-y) it looks like a spiral, so how come a spiral multiplies by another spiral becomes z=1?

Because (A/B)*(B/A) = (A/A)*(B/B) = 1*1 = 1. Try it out with numbers. If you have [(x+y)/(x-y)]*[(x-y)/(x+y)], pick random numbers for x and y. For example, x=6 and y=2:

[(6+2)/(6-2)]*[(6-2)/(6+2)] = [8/4]*[4/8] = *[1/2] = 1.

Also get me a chart on x-y=z, many thanks

Edited by elfmotat
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With different parentheses it could mean $(\frac{x+y}{x-y})^2$

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With different parentheses it could mean $(\frac{x+y}{x-y})^2$

But it's clear from the context of his post that that's not what he meant.

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With different parentheses it could mean $(\frac{x+y}{x-y})^2$

It looks really cool, looks like a portal or some sort, got any explanation for it ?

On another note my equation becomes (x+y)(x-y) on top and bottom, which looks like a saddle

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• 1 month later...

$\frac{x+y}{x-y}\times\frac{x-y}{x+y}$

$=\frac{\not x+\not y}{\not x-\not y}\times\frac{\not x-\not y}{\not x+\not y}$

$= 1 \times 1$

$= 1$

Edited by deesuwalka
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$\frac{x+y}{x-y}\times\frac{x-y}{x+y}$

$=\frac{\not x+\not y}{\not x-\not y}\times\frac{\not x-\not y}{\not x+\not y}$

$= 1 \times 1$

$= 1$

Provided neither x- y nor x+ y is equal to 0. That is, provided neither x= y nor x= -y. If x= y or x= -y, the expression is not defined.

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It looks really cool, looks like a portal or some sort, got any explanation for it ?

On another note my equation becomes (x+y)(x-y) on top and bottom, which looks like a saddle

$(x+y)/(x-y)*(x-y)/(x+y) could = (x+y)/[(x-y)^2/(x+y)]$

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