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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