(1) From the characteristics of the above equations and solutions, we can guess that:

The solution of the equation x+m/x=c+m/c(m≠0) about x is: X 1 = C, x2 = m/c.

The verification is as follows: when x 1 = c, the left side of the equation =c+m/c= right side, which holds;

When X2 = m/c, the left side of the equation = m/c+m/(m/c) = m/c+m× (c/m) = m/c+c = c+m/c = right side, which holds.

That is to say, the solution of the equation x+m/x=c+m/c(m≠0) about x is: X 1 = C, x2 = m/c.

(2) a≠ 1 It is easy to know from the meaning of the question, then:

The equation y+(2/y-1) = a+(2/a-1) can be changed to:

y- 1+2/(y- 1)= a- 1+2/(a- 1)

Let x=y- 1 and c=a- 1, then the original equation can be transformed into:

x+ 2/x =c +2/c

Then from the conclusion of 1

The solution of the equation x+ 2/x =c +2/c is: x 1 = c, and x 2 = 2/c.

Because x=y- 1 and c=a- 1, therefore:

Y 1- 1 = A- 1, Y 2- 1 = 2/(A- 1) that is, y 2 = 2/(a-1)+/kloc-0.

That is, the solution of the equation y+(2/y-1) = a+(2/a-1) is:

y①=a，y②=(a+ 1)/(a- 1)