八年级下册数学先化简再求值问题题目 （a-2/a²-2a-a-1/a²+4a+4）÷a-4/a+2 其中a满足a²+2a+1=0 怎么解，详细的解题步骤
2019-04-13
八年级下册数学先化简再求值问题题目 （a-2/a²-2a-a-1/a²+4a+4）÷a-4/a+2 其中a满足a²+2a+1=0 怎么解，详细的解题步骤
优质解答
a²+2a-1=0 a²+2a=1 原式=[(a-2)/a(a+2)-(a-1)/(a+2)²]×(a+2)/(a-4) ={[(a-2)(a+2)-a(a-1)]/a(a+2)²}×(a+2)/(a-4) =(a²-4-a²+a)(a+2)/[a(a-4)(a+2)²] =(a-24)(a+2)/[a(a-4)(a+2)²] =1/(a²+2a) =1/1 =1
a²+2a-1=0 a²+2a=1 原式=[(a-2)/a(a+2)-(a-1)/(a+2)²]×(a+2)/(a-4) ={[(a-2)(a+2)-a(a-1)]/a(a+2)²}×(a+2)/(a-4) =(a²-4-a²+a)(a+2)/[a(a-4)(a+2)²] =(a-24)(a+2)/[a(a-4)(a+2)²] =1/(a²+2a) =1/1 =1