Taking random values will not do

Algebra Level 3

x+1yz=15y+1xz=115z+1xy=13\large{\begin{aligned}x+\dfrac{1}{yz} &= \dfrac{1}{5}\\ y+\dfrac{1}{xz} &= -\dfrac{1}{15}\\ z+\dfrac{1}{xy} & =\dfrac{1}{3} \end{aligned}} If x,yx,y and zz are real numbers which satisfy the given equations above, find zyzx\dfrac{z-y}{z-x}.

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