例1解关于x的方程(x-a)/b+b/(x-a)=(x-b)/a+a/(x-b)(a≠b)分析此题若用通常方法来解,就会遇到去分母的繁琐运算和因去分母而出现的高次方程,若采用“倒数换元法”来解,方便快捷.解设x-a/b=t,x-b/a=m,则原方程可化 Example 1 solve the equation for x (xa) / b + b / (xa) = (xb) / a + a / (xb) (a ≠ b) Analysis of the problem If you use the usual method to solve, The cumbersome operation of the denominator and the higher order equation due to the denominator can be easily and quickly solved by using the “reciprocal transformation method.” The original equation can be solved by solving xa / b = t and xb / a = m