Question

Решить дробно-рациональное уравнение:

Answer 1

x^2 -1 =(x -1)(x+1)


(6 -2(x+1)) /(x-1)(x+1) =(2(x+1)-(x-4))/(x+1)

(6 -2x -2)/(x-1)(x+1) =(2x+2 -x+4)/(x+1)

(4 -2x)/(x-1)(x+1) =(x-2)/(x+1)

(4 -2x -(x-2)(x-1)) /(x-1)(x+1) =0

4 -2x -(x^2 -3x +2) =0

4 -2x -x^2 +3x -2 =0

-x^2 +x +2 =0; *(-1)

x^2 -x -2 =0

D =1 +8 =9 =3^2

x1 =(1 -3)/2 = -1

x2 =(1+3)/2 =2

ответ: x= -1; x =2