[(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)

[(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)