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Thanks. I will try working on it now.

@KingGeorge didn't get the solution :(

Okay.

We need \(x>1\) and \(3>y\) and \(4−y>\frac{x}{x−1}\). We also need \(z>1\), \(3>x\), and \(4−x>\frac{z}{z−1}\). Combine all of these things together, we get the following criteria.\[1

and \(z<4\) of course.

Another way to finish the proof would be to show \(z\geq3\).

In other words, if \(y\leq 5/3\), we are done.

That is also an excellent way one could do this.