Quy đồng mẫu thức ba phân thức
\({x \over {{x^2} – 2xy + {y^2} – {z^2}}}\), \({y \over {{y^2} – 2yz + {z^2} – {x^2}}}\) , \({z \over {{z^2} – 2zx + {x^2} – {y^2}}}\)
\(\eqalign{ & {x^2} – 2xy + {y^2} – {z^2} = {\left( {x – y} \right)^2} – {z^2} = \left( {x – y + z} \right)\left( {x – y – z} \right) \cr & {y^2} – 2yz + {z^2} – {x^2} = \left( {y – z + x} \right)\left( {y – z – x} \right) \cr & = – \left( {x – y + z} \right)\left( {x + y – z} \right) \cr & {z^2} – 2xz + {x^2} – {y^2} = {\left( {x – z} \right)^2} – {y^2} = \left( {x – z + y} \right)\left( {x – z – y} \right) = \left( {x + y – z} \right)\left( {x – y – z} \right) \cr} \)
MTC =\(\left( {x – y + z} \right)\left( {x + y – z} \right)\left( {x – y – z} \right)\)
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\(\eqalign{ & {x \over {{x^2} – 2xy + {y^2} – {z^2}}} = {x \over {\left( {x – y + z} \right)\left( {x – y – z} \right)}} = {{x\left( {x + y – z} \right)} \over {\left( {x – y + z} \right)\left( {x + y – z} \right)\left( {x – y – z} \right)}} \cr & {y \over {{y^2} – 2yz + {z^2} – {x^2}}} = {y \over {\left( {y – z + x} \right)\left( {y – z – x} \right)}} = {{ – y} \over {\left( {x – y + z} \right)\left( {x + y – z} \right)}} \cr & = {{ – y\left( {x – y – z} \right)} \over {\left( {x – y + z} \right)\left( {x + y – z} \right)\left( {x – y – z} \right)}} \cr & {z \over {{z^2} – 2zx + {x^2} – {y^2}}} = {z \over {\left( {x + y – z} \right)\left( {x – y – z} \right)}} = {{z\left( {x – y + z} \right)} \over {\left( {x + y – z} \right)\left( {x – y + z} \right)\left( {x – y – z} \right)}} \cr} \)