Thực hiện phép tính:

f) \(\frac{{x - 2}}{{x + 1}}:\frac{{{x^2} - 5x + 6}}{{{x^2} - 2x - 3}}.\)

j) \(1 + \frac{{{x^3} - x}}{{{x^2} + 1}} \cdot \left( {\frac{1}{{1 - x}} - \frac{1}{{1 - {x^2}}}} \right)\)

\( = 1 + \frac{{x\left( {{x^2} - 1} \right)}}{{{x^2} + 1}} \cdot \left[ {\frac{1}{{1 - x}} - \frac{1}{{\left( {1 - x} \right)\left( {1 + x} \right)}}} \right]\)

\( = 1 - \frac{{x\left( {1 - {x^2}} \right)}}{{{x^2} + 1}} \cdot \frac{{1 + x - 1}}{{\left( {1 - x} \right)\left( {1 + x} \right)}}\)
\( = 1 - \frac{{x\left( {1 - x} \right)\left( {1 + x} \right)}}{{{x^2} + 1}} \cdot \frac{x}{{\left( {1 - x} \right)\left( {1 + x} \right)}}\)

a) \(\left( {x + 2} \right)\left( {x + 3} \right) - x\left( {x + 6} \right) = 4\)

\({x^2} + 3x + 2x + 6 - {x^2} - 6x = 4\)

\( - x + 6 = 4\)

\( - x = - 2\)

\(x = 2\).