Sum of fractions, again

Algebra Level 5

$\large\frac{x(yz+1)^2}{z^2(zx+1)}+\frac{y(zx+1)^2}{x^2(xy+1)}+\frac{z(xy+1)^2}{y^2(yz+1)}$

Let $$x,y,z>0$$ satisfy $$x+y+z\leq\frac{3}{2}$$. If the minimum value of the expression above can be written as $$\dfrac{a}{b}$$ which $$a$$ and $$b$$ are coprime positive integers, calculate the product $$ab$$.

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