Question

解方程 x² -6/x-4 + 2(x-4)/x² -6 =3

Answer 1

答：

(x^2-6)/(x-4)+2(x-4)/(x^2-6)=3

设：m=(x^2-6)/(x-4)

则原方程化为：m+2/m=3

m^2-3m+2=0

(m-1)(m-2)=0

m=1或者m=2

1）m=(x^2-6)/(x-4)=1

x^2-6=x-4

x^2-x-2=0

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

x=-1或者x=2

2）m=(x^2-6)/(x-4)=2

x^2-6=2x-8

x^2-2x+2=0

方程无实数解

经检验,x=-1和x=2是方程的解