先化简再求值：[(2x+6)/(x^2-4x+4)]÷(x+3)×[(x-2)/(x+3)],其中x=3

题目

先化简再求值：[(2x+6)/(x^2-4x+4)]÷(x+3)×[(x-2)/(x+3)],其中x=3

答案

原式=2(x+3)/(x-2)²*1/(x+3)*(x-2)/(x+3)
=2/(x-2)²*(x-2)/(x+3)
=2/(x-2)(x+3)
=2/(1*6)
=1/3