\(A = \frac{{yz}}{{\left( {x - y} \right)\left( {x - z} \right)}} + \frac{{zx}}{{\left( {y - z} \right)\left( {y - x} \right)}} + \frac{{xy}}{{\left( {z - x} \right)\left( {z - y} \right)}}\)

\( = \frac{{ - yz\left( {y - z} \right) - zx\left( {z - x} \right) - xy\left( {x - y} \right)}}{{\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)}}\)

\( = \frac{{ - {y^2}z + {z^2} - {z^2}x + {x^2}z - {x^2}y + {x^2}}}{{\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)}}\)

\( = \frac{{ - {y^2}\left( {z - x} \right) + y\left( {{z^2} - {x^2}} \right) - zx\left( {z - x} \right)}}{{\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)}}\)

\( = \frac{{\left( {z - x} \right)\left( { - {y^2} + yz + yx - zx} \right)}}{{\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)}}\)

\( = \frac{{\left( {z - x} \right)\left[ { - y\left( {y - z} \right) + x\left( {y - z} \right)} \right]}}{{\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)}}\)

\( = \frac{{\left( {z - x} \right)\left( {y - z} \right)\left( {x - y} \right)}}{{\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)}} = 1\)

Vậy A = 1