Question

Answer to solving equation

Answer 1

x = 5 or x = (-1)

Explanation:

`(x)/(x + 1) - (2)/(x - 2) = \frac{3}{ {x}^(2) - x - 2 } \\ (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 \\`

(x - 5) = 0 or (x + 1) = 0 should be.

x = 5 or x = -1