Ta có:
+) \( {x^2} - 2xy + {y^2} - {z^2}\)\(\, = {\left( {x - y} \right)^2} - {z^2} \)\(\,= \left( {x - y + z} \right)\left( {x - y - z} \right) \)
+) \({y^2} - 2yz + {z^2} - {x^2}\)\(\, = {\left( {y - z} \right)^2} - {x^2}\)\(\, = \left( {y - z + x} \right)\left( {y - z - x} \right) \)\(\, = - \left( {x - y + z} \right)\left( {x + y - z} \right) \)
+) \({z^2} - 2xz + {x^2} - {y^2} = {\left( {x - z} \right)^2} - {y^2}\)\(\, = \left( {x - z + y} \right)\left( {x - z - y} \right) \)\(\,= \left( {x + y - z} \right)\left( {x - y - z} \right) \)
MTC =\(\left( {x - y + z} \right)\left( {x + y - z} \right)\left( {x - y - z} \right)\)
\( \displaystyle{x \over {{x^2} - 2xy + {y^2} - {z^2}}} \)\(\,\displaystyle= {x \over {\left( {x - y + z} \right)\left( {x - y - z} \right)}}\)\(\, \displaystyle= {{x\left( {x + y - z} \right)} \over {\left( {x - y + z} \right)\left( {x + y - z} \right)\left( {x - y - z} \right)}} \)
\(\displaystyle{y \over {{y^2} - 2yz + {z^2} - {x^2}}} \)\(\,\displaystyle= {y \over {\left( {y - z + x} \right)\left( {y - z - x} \right)}} \)\(\,\displaystyle= {{ - y} \over {\left( {x - y + z} \right)\left( {x + y - z} \right)}} \)\(\, \displaystyle= {{ - y\left( {x - y - z} \right)} \over {\left( {x - y + z} \right)\left( {x + y - z} \right)\left( {x - y - z} \right)}} \)
\(\displaystyle{z \over {{z^2} - 2zx + {x^2} - {y^2}}} \)\(\,\displaystyle= {z \over {\left( {x + y - z} \right)\left( {x - y - z} \right)}}\)\(\, \displaystyle= {{z\left( {x - y + z} \right)} \over {\left( {x + y - z} \right)\left( {x - y + z} \right)\left( {x - y - z} \right)}} \)
