Question

(x +1)/(x -1) + (x -2)/(x +2) = 3, x≠1,

Answer 1

Answer:

$\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 3, x≠1$

$→ \frac{(x + 1)(x + 2) + (x - 2)(x - 1)}{(x - 1)(x + 2)} = 3$

$→ \frac{ {x}^{2} + 2 x + x + 2 + {x }^{2} - x - 2x + 2}{ {x}^{2} + 2x - x - 2 } = 3$

$→ \frac{2 {x}^{2} + 4}{ {x}^{2} + x - 2} = 3$

$→2 {x}^{2} + 4 = 3( {x}^{2} + x - 2)$

$→2 {x}^{2} + 4= 3 {x}^{2} + 3x - 6$

$→2 {x}^{2} - 3 {x}^{2} - 3x + 4 + 6 = 0$

$→ - {x}^{2} - 3x + 10 = 0$

$→ {x}^{2} + 3x - 10 = 0$

$→{x}^{2} + 5x - 2x - 10 = 0$

$→x(x + 5) - 2(x + 5) = 0$

$→(x + 5)(x - 2) = 0$

$→x + 5 = 0 \: or \: x - 2 = 0$

$→x = - 5 \: or \: x = 2$