作业帮[(a²-4）/（a²-4a+4)+(2-a)/(a+2)]除以a/(a-2)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/12 01:15:25
![[(a²-4）/（a²-4a+4)+(2-a)/(a+2)]除以a/(a-2)](/uploads/image/z/1564119-63-9.jpg?t=%5B%28a%26%23178%3B-4%EF%BC%89%2F%EF%BC%88a%26%23178%3B-4a%2B4%29%2B%282-a%29%2F%28a%2B2%29%5D%E9%99%A4%E4%BB%A5a%2F%28a-2%29)
[(a²-4）/（a²-4a+4)+(2-a)/(a+2)]除以a/(a-2)
[(a²-4）/（a²-4a+4)+(2-a)/(a+2)]除以a/(a-2)
[(a²-4）/（a²-4a+4)+(2-a)/(a+2)]除以a/(a-2)
原式=[ (a+2) (a-2) / (a-2)² + (2-a) / (a+2) ] / [ a / (a-2) ] (a≠2)
=[ (a+2) / (a-2) -(a-2) / (a+2) ] · [ (a-2) / a ] (a≠0)
=[ (a+2)²-(a-2)² / (a+2) (a-2) ] · [ (a-2) / a ]
=[ 8a / (a+2) (a-2) ] · [ (a-2) / a ]
=8 / (a+2)
a²-4=(a+2) (a-2)
a²-4a+4=(a-2)²
+ (2-a)=-(a-2)