x+1/x=2+1/2的解为x1=2,x2=1/2 .x+1/x=3+1/3的解为x1=3,x2=1/3 .x+1/x=

这简单,等式两边同时减1,右边就是（a-1）+【1/（a-1）】了,左边你通分,肯等能得到（x-1）+【1/（x-1）】,我没算,但是肯定是.然后结果就是,x1=a-1,x2=1/（a-1）.我这输入法……

这个规律为,如果：
x+1/x=a+1/a
则它的解为
x1=a,x2=1/a
x+1/(x-1)=a+1/(a-1)
x-1+1/(x-1)=a-1+1/(a-1)
根据以上规律可得：
x-1=a-1或x-1=1/(a-1)
所以这个方程的解为：
x1=a ,x2=1/(a-1)+1
即：x1=a ,x2=a/(a-1)

方程x+2/x-1=a+2/a-1
化为：(x-1)+2/(x-1)=(a-1)+2/(a-1)
再化为：(x-1)/√2+1/[(x-1)/√2]=(a-1)/√2+2/[(a-1)/√2]
把(x-1)/√2,及(a-1)/√2看成一个整体,应用规律,（x-1）/√2=(a-1)/√2,及(x-1)/√2=√2/(a-1)
即x=a,及x=2/(a-1)+1=(a+1)/(a-1)

(1)x1=c.x2=m/c
(2)等式两边同时减一.得x-1+2/(x-1)=a-1+2/(a-1)所以(x-1)1=a-1.即x1=a.(x-1)2=2/(a-2)即x2=1+2/(a一1)=(a+1)/(a-1)

解
【1】
x²-x+1
=(x²-2x+1)+x
=(x-1)²+x
=(x-1)²+(x-1)+1
即：x²-x+1=(x-1)²+(x-1)+1
∴(x²-x+1)/(x-1)=[(x-1)²+(x-1)+1]/(x-1)=(x-1)+1+[1/(x-1)]
即原方程左边=（x-1)+1+[1/(x-1)]
原方程可化为：
(x-1)+1+[1/(x-1)]=a+[1/(a-1)]
移项可得：
(x-1)+[1/(x-1)]=(a-1)+[1/(a-1)]
令x-1=y,a-1=c.上面方程可化为：
y+(1/y)=c+(1/c)
【2】
此时,方程：
(x-1)+[1/(x-1)]=(a-1)+[1/(a-1)]的解为：
x₁-1=a-1 x₂-1=1/(a-1)
即：x₁=a.x₂=a/(a-1)

x+1/(x-2)=c+1/(c-2)
x-2+1/(x-2)+2=c+1/(c-2)
x-2+1/(x-2)=（c-2）+1/(c-2)
所以x-2=c-2
所以X1=C,X2=1/C.

x +1/(x+1)=a+ 1/(a+1)
x-a-[1/(a+1) -1/(x+1)]=0
x-a- [(x+1)-(a+1)]/[(x+1)(a+1)]=0
(x-a)- (x-a)/[(x+1)(a+1)]=0
(x-a)[1- 1/[(x+1)(a+1)]]=0
(x-a)[(a+1)(x+1) -1]=0 /这一步是等式两边同乘以(x+1)(a+1)
x-a=0或(a+1)(x+1)-1=0
x-a=0 x=a
(a+1)(x+1)-1=0 x=1/(a+1) -1=(1-a-1)/(a+1)=-a/(a+1)
综上,得
x=a或x= -a/(a+1)