定理关于x的方程x+nx=a+na(an≠0)的解为x=a或x=na.证明:将原方程去分母,得ax2+an=a2x+nx,即ax2-(a2+n)x+an=0,所以(x-a)(ax-n)=0,解得x=a或x=na.经检验,x=a和x=na都是原方程的解.由这个定理,可以得到下面的推论.推论关于x的方程x+1x=a+a1的解为x=a或x=1a.掌握上述定理和推论, Theorem The solution to x for x+nx=a+na(an≠0) is x=a or x=na. Proof: Denominator to the original equation, get ax2+an=a2x+nx, ie ax2-(a2) +n)x + an = 0, so (xa) (ax-n) = 0, the solution is x = a or x = na. After testing, x = a and x = na are all solutions of the original equation. Theorem, you can get the following inferences. Inference about the equation of x x+1x=a+a1 is x=a or x=1a. Master the above theorems and inferences,