化简((x+2)/(x^2-2x)+8/(4-x^2))÷(x-2)/2为什么我化简之后很复杂?记得带上过程_数学解答

化简((x+2)/(x^2-2x)+8/(4-x^2))÷(x-2)/2
为什么我化简之后很复杂?
记得带上过程

人气：327 ℃　时间：2020-06-19 08:32:19

解答

[(x+2)/(x^2-2x)+8/(4-x^2)]÷(x-2)/2
={ (x+2)/[x(x-2)]- 8/[(x-2)(x+2)] }*2/(x-2)
={ [(x+2)平方-8x]/[x(x-2)(x+2)] }*2/(x-2)
={ (x平方-4x+4)/[x(x-2)(x+2)] }*2/(x-2)
={ (x-2)平方/[x(x-2)(x+2)] }*2/(x-2)
=2/[x(x+2)]