Question

x+1/x-1 + x-2/x+1 = 3​

Answer 1

$\frac{x + 1}{x - 1} + \frac{x - 2}{x + 1} = 3 \\ \frac{(x + 1)(x + 1) + (x - 2)(x - 1)}{(x - 1)(x + 1)} = 3 \\ \frac{ {(x + 1)}^{2} + {x}^{2} - x - 2x + 2 }{ {x}^{2} - {1}^{2} } = 3\\ \frac{ {x}^{2} + {1}^{2} + 2 \times x \times 1 + {x }^{2} - 3x + 2}{ {x}^{2} - 1 } = 3\\ 2 {x}^{2} + 1 + 2x - 3x + 2 = 3( {x}^{2} - 1) \\ 2 {x}^{2} - x + 3 = 3 {x}^{2} - 3 \\ 3 {x}^{2} - 3 - 2 {x}^{2} + x - 3 = 0 \\ {x}^{2} + x - 6 = 0 \\ {x}^{2} + (3 - 2)x - 6 = 0 \\ {x}^{2} + 3x - 2x - 6 = 0 \\ x(x + 3) - 2(x + 3) = 0 \\( x + 3)(x - 2) = 0 \\ x + 3 = 0 \\ x = - 3 \\ x - 2 = 0 \\ x = 2 \\ x = 2 \: and - 3$