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Say you have $dy/dx = x$, is it valid to write $dy/x = dx$?

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    Yes (for the most part, anyway). Not sure why you'd want to write it like that though. You can turn it into an integration by having both x on one side. – 2017-01-16
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    i would write $$dy=xdx$$ – 2017-01-16
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    I understand that dy=xdx is valid, but I'm just asking IF it is mathematically incorrect (or invalid) to write dy/x = dx – 2017-01-16
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    It is correct, but it unusable. – 2017-01-16

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You can do that, but why would you want to?

With $\frac{dy}{dx}=x$ you can just integrate with respect to x to get $y=\frac{x^2}{2}+C.$

(if you want to be completionist then $\frac{dy}{dx}=x$ turns into $dy=x\ dx$)