A very simple question concerning the algebra of physics

[help1please]

Suppose I had an expression, for the sake of this post

$$\frac{Ec^2}{mv}$$

we know that $$c^2 = \frac{E}{m}$$ so can the above expression be substituted as

$$c^2 \frac{c^2}{v}$$

Yes, yes, I know this result is very uninteresting, I was just making a quick example. Thank you!

 

[help1please]

I ask this because some work I am following states that if two particles are really close separated at a distance R then the momentum is large proportional to

$$\frac{\hbar}{R}$$

Then it says that using a substitution then in E=pc

$$E= \frac{\hbar c}{R}$$

so in this sense, if you can do it that way, you can also do it my way, the reversed way in the OP, right?

 

[Dick]

Suppose I had an expression, for the sake of this post

$$\frac{Ec^2}{mv}$$

we know that $$c^2 = \frac{E}{m}$$ so can the above expression be substituted as

$$c^2 \frac{c^2}{v}$$

Yes, yes, I know this result is very uninteresting, I was just making a quick example. Thank you!

So far so good. Is that the whole question? You can always substitute equal for equals.

 

[help1please]

Thank you, that is all I wanted to know! :)