Giải phương trình:

a) \(\left( {\frac{1}{x} + 2} \right) = \left( {\frac{1}{x} + 2} \right)\left( {{x^2} + 1} \right)\);                

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

Giải các phương trình:

a) \(\frac{{2x - 1}}{{x - 1}} + 1 = \frac{1}{{x - 1}}\)         b) \(\frac{{5x}}{{2x + 2}} + 1 = - \frac{6}{{x + 1}}\)

c) \(x + \frac{1}{x} = {x^2} + \frac{1}{{{x^2}}}\) d) \(\frac{{x + 3}}{{x + 1}} + \frac{{x - 3}}{x} = 2\).

Giải các phương trình sau:

a) \(\frac{1}{{x - 2}} + 3 = \frac{{3 - x}}{{x - 2}}\);          b) \(\frac{{3x - 2}}{{x + 7}} = \frac{{6x + 1}}{{2x - 3}}\);

c) \(\frac{{x + 1}}{{x - 1}} - \frac{{x - 1}}{{x + 1}} = \frac{4}{{{x^2} - 1}}\);                                           d) \(2x - \frac{{2{x^2}}}{{x + 3}} = \frac{{4x}}{{x + 3}} + \frac{2}{7}\).

Giải các phương trình:

a) \(\frac{{2x - 5}}{{x + 5}} = 3\);                         

b) \(\frac{{{x^2} - 6}}{x} = x + \frac{3}{2}\);           

c) \(\frac{{\left( {{x^2} + 2x} \right) - (3x + 6)}}{{x - 3}} = 0\);                                                                          

d) \(\frac{5}{{3x + 2}} = 2x - 1\).

a) \(\frac{1}{{x - 1}} - \frac{{3{x^2}}}{{{x^3} - 1}} = \frac{{2x}}{{{x^2} + x + 1}}\)                      b) \(\frac{3}{{(x - 1)(x - 2)}} + \frac{2}{{(x - 3)(x - 1)}} = \frac{1}{{(x - 2)(x - 3)}}\)

c) \(1 + \frac{1}{{x + 2}} = \frac{{12}}{{8 + {x^3}}}\)     d) \(\frac{{13}}{{(x - 3)(2x + 7)}} + \frac{1}{{2x + 7}} = \frac{6}{{(x - 3)(x + 3)}}\).