Răspuns:
[tex] \frac{x - 5}{x - 3} [/tex]
Explicație pas cu pas:
[tex] \frac{ {x}^{2} - 3x - 10}{ {x}^{2} - x - 6 } + \frac{2x}{2 {x}^{2} - 6x } = \\ \frac{ {x}^{2} - 5x + 2x - 10}{ {x}^{2} - 3x + 2x - 6 } + \frac{2x}{2x(x - 3)} = \\ \frac{x(x + 2) - 5(x + 2)}{x(x + 2) - 3(x + 2)} + \frac{1}{x - 3} = \\ \frac{(x - 5)(x + 2)}{(x - 3)(x + 2)} + \frac{1}{x - 3} = \\ \frac{x - 5}{x - 3} + \frac{1}{x - 3} = \frac{x - 5}{x - 3} [/tex]
x²-x-6 = x²+2x-3x-6 = x(x+2)-3(x+2) = (x+2)(x-3)
x²-3x-10 = x²+2x-5x-10 = x(x+2)-5(x+2) = (x+2)(x-5)
2x²-6x = 2x(x-3)
E(x) = (x-4)/(x-3) , (∀) x ∈ R - {-2 , 0 , 3 , 5}
