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

Ta có:

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

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