Right Triangle's Variable Sides

Geometry Level 2

In a certain right triangle, the hypotenuse equals $$(x+z)$$ while the other two sides are $$(x+y)$$ and $$(y+z)$$ for positive integers $$x, y, z$$.

If $$y+4=z$$ and $$z>x$$ , then compute $$\dfrac{z}{x}$$.

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