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If I know $x$ divided by $y,$ how can I work out $x-y$ from that? Suppose $x>y.$ Is this even possible? Thanks in advance.

Michael Hardy
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crvcio
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    Say $\frac{x}{y}=z$. This implies $x=yz$ , hence we get $x-y=yz-y=y(z-1)$ But without any further information we cannot determine $x-y$. If we , for example , know $y$ , we can do it. – Peter Jul 05 '21 at 17:57
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    In the special case $\frac{x}{y}=1$ , we can actually determine $x-y$. It is $0$ in this case because we have $x=y$. – Peter Jul 05 '21 at 17:59
  • If you knew both $x-y$ and $x/y$, then by a standard argument you would know both $x$ and $y$ as separate values. So one way to think about this is you need two equations to determine two unknowns. – hardmath Jul 05 '21 at 18:01

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Note that $\frac{4}{2} = \frac{2}{1}$, but $4-2=2 \neq 1 = 2-1$.

So the answer to your question is negative

Mario G
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