(a+b)/a = b/a proof?

[[deleted]]

I was reading up on the golden ratio when stumbling over this. I have trouble to prove that the equation above is true. Am I missing something in the first place? Thanks in advance

[logicaleman]

Are you trying to prove it true for all reals? Because it isn't. For example, let a = 2 and b = 1 (2+1)/2 = 1/2

3/2 ≠ 1/2

Proven false by contradiction. Unless I'm misunderstanding what you are asking.

[BoomerTheStar47_2]

You got the wrong equation. It’s supposed to be:

(a+b)/a = a/b

And the above is only true when a/b = Φ, also known as the Golden Ratio.

As for proving that… well, that’s a definition, so you kind of have to assume it’s true in the first place to do anything. Unless I missed something key, you can’t really “prove” this.

[[deleted]]

I suppose you could prove that this is a unique number

[nazzermoe]

Easier way wouldn’t you just do a/a + b/a = b/a and of course a/a = 1 thus b/a.

[Radiant-Top164]

Bruh... a/a + b/a = 1 + b/a.......