variational lower bound confusion

In this blog describing variational inference under the section KL divergence and ELBO

they mention that in the equation

$$p(x) = \frac{w(x)}{Z}$$

we can substitute $$w$$ and $$Z$$ with:

$$Z = p(x;\theta)$$ $$w = p(x,z;\theta)$$

However that would imply (after substitution) that:

$$p(x) = \frac{p(x,z;\theta)}{p(x;\theta)}$$

which does not look correct. However I think I am missing something. Can anyone shed some light on this?

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