Răspuns:
Bună,
[tex] \frac{3x}{x + 2} + \frac{6x + 4}{ {x}^{2} - 4} - \frac{2x}{x - 2} = \\ \frac{3x(x - 2)}{(x + 2)(x - 2)} + \frac{6x + 4}{(x - 2)(x + 2)} - \frac{2x(x + 2)}{(x - 2)(x + 2)} = \\ \frac{3 {x}^{2} - 6 + 6x + 4 - 2 {x}^{2} - 4x }{(x - 2)(x + 2)} = \\ \frac{ {x}^{2} - 4x + 4 }{(x - 2)(x + 2)} = \\ \frac{(x - 2) ^{2} }{(x - 2)(x + 2)} = \\ \frac{x - 2}{x + 2} [/tex]
[tex] \frac{9 - 15x}{ {x}^{2} - 9 } + \frac{4x}{x - 3} - \frac{3x}{x +3 } = \\ \frac{9 - 15x}{(x - 3)(x + 3)} + \frac{4x(x + 3)}{(x - 3)(x + 3)} - \frac{3x(x - 3)}{(x + 3)(x - 3)} = \\ \frac{9 - 15x + 4{x}^{2} + 12x - 3 {x}^{2} + 9x }{(x - 3)(x + 3)} = \\ \frac{9 + 6x + x ^{2} }{(x - 3)(x + 3)} = \\ \frac{{(3 + x})^{2} }{(x - 3)(x + 3)} = \\ \frac{3 + x}{x - 3} [/tex]
[tex] \frac{4x}{x - 5} - \frac{4 {x}^{2} + 10x }{ {x}^{2} - 25 } + \frac{x}{x + 5} = \\ \frac{4x(x + 5)}{(x - 5)(x + 5)} - \frac{4 {x}^{2} + 10x }{(x - 5)(x + 5)} + \frac{x(x - 5)}{(x + 5)(x - 5)} = \\ \frac{4 {x}^{2} + 20x - 4x ^{2} - 10x + {x}^{2} - 5x }{(x + 5)(x - 5)} = \\ \frac{5x + {x}^{2} }{(x + 5)(x - 5)} = \\ \frac{x(x + 5)}{(x + 5)(x - 5)} = \\ \frac{x}{x - 5} [/tex]
[tex] \frac{3x}{2x + 1} + \frac{x - 2}{1 - 2x} - \frac{4x + 1}{4 {x}^{2} - 1} = \\ \frac{3x}{2x + 1} - \frac{x - 2}{2x - 1} - \frac{4x + 1}{(2x - 1)(2x + 1)} = \\ \frac{3x(2x - 1)}{(2x - 1)(2x + 1)} - \frac{(x - 2)(2x + 1)}{(2x -1)(2x + 1)} - \frac{4x + 1}{(2x - 1)(2x + 1)} = \\ \frac{6 {x}^{2} - 3x - 2x + 3x + 2 - 4x - 1 }{(2x - 1)(2x + 1)} = \\ \frac{4x ^{2} - 4x + 1 }{(2x - 1)(2x + 1)} = \\ \frac{(2x - 1) ^{2} }{(2x - 1)(2 x + 1)} = \\ \frac{2x - 1}{2x + 1} [/tex]
Sper că te-am ajutat
