Cho phân thức $P = \frac{{{x^2} - 4x + 3}}{{{x^2} - 9}}$.

Ta có:

$P = \frac{{{x^2} - 4x + 3}}{{{x^2} - 9}} = \frac{{{x^2} - 3x - x + 3}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} = \frac{{\left( {{x^2} - 3x} \right) - \left( {x - 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}}$

$= \frac{{x\left( {x - 3} \right) - \left( {x - 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} = \frac{{\left( {x - 3} \right)\left( {x - 1} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} = \frac{{x - 1}}{{x + 3}}$.