2)

[tex] \frac{6x + 7}{1 - 2x} - \frac{5x - 4}{2x - 1} = - \frac{6x + 7}{2x - 1} - \frac{5x - 4}{2x - 1} = \\ \frac{ - (6x + 7) - (5x - 4)}{2x - 1} = \frac{ - 6x - 7 - 5x + 4}{2x - 1} = \\ \frac{ - 11x - 3}{2x - 1} = - \frac{11x + 3}{2x - 1} [/tex]

3)

[tex] \frac{3}{x} + \frac{4x - 3}{x - 1} = \frac{3(x - 1) + x(4x - 3)}{x(x - 1)} = \\ \frac{3x - 3 + 4 {x}^{2} - 3x}{x(x - 1)} = \frac{4 {x}^{2} - 3 }{ {x}^{2} - x } [/tex]

4)

[tex] \frac{3x - 1}{ {x}^{2} + 2x } - \frac{3}{x - 2} + \frac{5}{x} = \\ \frac{3x - 1}{x(x + 2)} - \frac{3}{x - 2 } + \frac{5}{x} = \\ \frac{(3x - 1)(x - 2) - 3x(x + 2) + 5(x {}^{2} - 4) }{x(x + 2)(x - 2)} = \\ \frac{3 {x}^{2} - 6x - x + 2 - 3 {x}^{2} - 6x + 5 {x}^{2} - 20 }{x(x {}^{2} - 4 )} = \\ \frac{5 {x}^{2} - 13x - 18x }{ {x}^{3} - 4x } [/tex]

5)

[tex] \frac{2}{ {x}^{2} - 9 } + \frac{1}{x - 3} - \frac{2}{x + 3} = \\ \frac{2}{(x - 3)(x + 3)} + \frac{1}{x - 3} - \frac{2}{x + 3} = \\ \frac{2 + x + 3 - 2(x - 3)}{(x - 3)(x + 3)} = \\ \frac{5 + x - 2x + 6}{ {x}^{2} - 9} = \frac{ - x + 11}{ {x}^{2} - 9} [/tex]