如何解可化为一元二次方程的方程x+(1/x)=c+(1/c)（关于x的方程，c≠0）？按照通常的解法，是将分式方程化为整式方程，即cx~2-（c~2+1）x+c=0，解关于x的一元二次方程得x_1=c，x_2=(1/c)经检验知x_1=c，x_2=(1/c)是原方程的解。笔者认为，倘若应用该题的结论，便可简化许多有关习题的解题过程。现举例如下：例1 解关于x的方程x+(1/(x-1))=a+(1/(a-1))。解：将原方程变形为 How to solve the equation x+(1/x)=c+(1/c) (the equation about x, c≠0) that can be converted into a quadratic equation? According to the usual solution, the fractional equation is transformed into the integral equation, ie, cx~2-(c~2+1)x+c=0, and the one-variable quadratic equation of the solution to x is x_1=c, x_2=(1). /c) It has been verified that x_1=c and x_2=(1/c) is the solution to the original equation. The author believes that if the conclusion of the problem is applied, the problem solving process of many problems can be simplified. An example is given below: Example 1 Solve the equation x about x (1/(x-1))=a+(1/(a-1)). Solution: Transform the original equation into