Verified answer

[tex]1.\frac{8x^{2} + 3 }{x} + \frac{5x^{2} - 3 }{x} = \frac{8x {}^{2} + 3 + 5x {}^{2} - 3}{x} = \frac{13x {}^{2} }{x} = 13x[/tex]

[tex]2.\frac{3x + 2}{4x - y} + \frac{2x - 1}{y - 4x} = \frac{3x + 2}{4x - y} - \frac{2x - 1}{4x - y} = \frac{3x + 2 - 2x + 1}{4x - y} = \frac{x + 3}{4x - y}[/tex]

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