The law is: the fractional equation in the form of x- 1/x=a- 1/a, and its solution is: x=a, x =-1/a. If there is no such form, it can be solved as long as the constant can be decomposed into a- 1/a.

Proved as follows:

x- 1/x=a- 1/a

Multiply both sides of the equation by ax at the same time and you get

Axe? -a=a？ x-x

Axe? +( 1-a？ )x-a=0

(ax+ 1)(x-a)=0

therefore

Ax+ 1=0, the solution is: x=- 1/a,

X-a=0, the solution is: x=a,

Therefore, any fractional equation of the form: x- 1/x=a- 1/a has two roots: x=a and x =-1/a.

Similarly, for a fractional equation in the form of x+ 1/x=a+ 1/a, its two roots are: x=a and x =1/a.

It can also be extended to the fractional equation in the form of x+k/x=a+k/a, and its solution is: x=a, x = k/a.