$$\frac{ { x }^{ 2 } +z+x(z-x)+ { z }^{ 2 } }{ zx(z-x) }$$
$\frac{x+z+1}{x\left(z-x\right)}$
$$\frac{z\left(x+z+1\right)}{xz\left(-x+z\right)}$$
$$\frac{x+z+1}{x\left(-x+z\right)}$$
$$\frac{x+z+1}{-x^{2}+xz}$$
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