Answer:
x = 5 or x = (-1)
Step-by-step explanation:
[tex] \frac{x}{x + 1} - \frac{2}{x - 2} = \frac{3}{ {x}^{2} - x - 2 } \\ \frac{x(x - 2) - 2(x + 1)}{(x + 1)(x - 2)} = \frac{3}{ {x}^{2} - x - 2 } \\ \frac{ {x}^{2} - 2x - 2x - 2}{x(x - 2) + 1(x - 2)} = \frac{3}{ {x}^{2} - x - 2} \\ \frac{ {x}^{2} - 4x - 2 }{ {x}^{2} - 2x + x - 2} = \frac{3}{ {x}^{2} - x - 2 } \\ \frac{ {x}^{2} - 4x - 2 }{ {x}^{2} - x - 2 } = \frac{3}{ {x}^{2} - x - 2} \\ ( {x}^{2} - 4x - 2)( {x}^{2} - x - 2) = 3( {x}^{2} - x - 2) \\ {x}^{2} - 4x - 2 = 3 \\ {x}^{2} - 4x - 2 - 3 = 0 \\ {x}^{2} - 4x - 5= 0 \\ {x}^{2} + x - 5x - 5 = 0 \\ x(x +1 ) - 5(x + 1) = 0 \\ (x - 5)(x + 1) = 0 \\ [/tex]
(x - 5) = 0 or (x + 1) = 0 should be.
x = 5 or x = -1
