1/( х( x + 2 )) - 1/( x + 1 ) ^2 = 1/12
X не равен ( - 2 ) ; ( - 1 )
( ( Х + 1 )^2 - х( Х + 2 ) ) / ( х( Х + 2)( Х + 1 )^2 = 1/12
( х^2 + 2х + 1 - х^2 - 2х ) / ( х( Х + 2 )( Х + 1 )^2 ) = 1/12
1/( х^2 + 2х )( х^2 + 2х + 1 ) = 1/12
12 = ( х^2 + 2х )( х^2 + 2х + 1 )
Х^2 + 2х = а
12 = а( а + 1 )
а^2 + а - 12 = 0
D = 1 + 48 = 49 = 7^2
a1 = ( - 1 + 7 ) : 2 = 3
a2 = ( - 1 - 7 ) : 2 = - 4
1) x^2 + 2x = 3
X^2 + 2x - 3 = 0
D = 4 + 12 = 16 = 4^2
X1 = ( - 2 + 4 ) : 2 = 1
X2 = ( - 2 - 4 ) : 2 = - 3
2) x^2 + 2x = - 4
X^2 + 2x + 4 = 0
D = 4 - 16 = - 12 ( < 0 )
Нет корней
Ответ 1 ; ( - 3 )