Question

Найдите корни уравнения (x-2/x+1)+(x+1/x-2)=4 1/4

Answer 1

$\frac{x-2}{x+1} + \frac{x+1}{x-2} = 4\frac{1}{4}$
ОДЗ: x ≠ -1, x ≠ 2
$\frac{x^2-4x+4+x^2+2x+1}{(x+1)(x-2)} = \frac{17}{4}$
$\frac{2x^2-2x+5}{(x+1)(x-2)} - \frac{17}{4} = 0$
$\frac{8x^2-8x+20-17x^2+17x+34}{4*(x+1)(x-2)} = 0$
$\frac{-9x^2+9x+54}{4(x+1)(x-2)} = 0$
$-9x^2 +9x+54 = 0$
делим на -9:
$x^2-x-6=0$
по теореме Виета x = 3 , x = -2