Question

当a=根号2+1时,求（a+1）/（a-1）×（a^2-4）/(a-1)^2 ÷ 1/（a^2-1）的值

Answer 1

（a+1）/（a-1）×（a^2-4）/(a-1)^2 ÷ 1/（a^2-1）=（a+1）/（a-1）×（a^2-4）/(a-1)^2 × （a-1）（a+1）=（（a+1）/(a-1)）^2 ×（a-2）（a+2）
把a的值代入，乘号左边=（根号2+1）^2 ,乘号右边=（根号231）（根号2-1），结合起来再用下平方差公式就很容易得出结果为（根号2+1）×（根号2+3）=5+4根号2

Answer 2

（a+1）/（a-1）×（a^2-4）/(a-1)^2 ÷ 1/（a^2-1）
=（a+1)/(a-1)×(a-2)(a+2)/(a-1)^2×(a-1)(a+1)
=(a+1)^2(a-2)(a+2)/(a-1)^2
=(√2+1+1)^2(√2+1-2)(√2+1+2)/(√2+1-1)^2
=(√2+2)^2(√2-1)(√2+3)/(√2+1-1)^2
=[√2(1+√2)]^2(√2-1)(√2+3)/(√2)^2
=2(√2+1)^2(√2-1)(√2+3)/2
=(√2+1)(2-1)(√2+3)
=2+3√2+√2+3
=5+4√2

Answer 3

式字有点乱，再加多个括号明确一下

Answer 4

22加16倍根号2，先约分在带值计算

Answer 5

（a+1）/（a-1）×（a^2-4）/(a-1)^2 ÷ 1/（a^2-1）
=（a+1)/(a-1)×(a-2)(a+2)/(a-1)²×(a-1)(a+1)
=(a+1)²(a-2)(a+2)/(a-1)²
=(√2+1)²(√2+1-2)(√2+1+2)/(√2-1+1)²
=(√2+1)(√2+3)/2
=(2+√2+3√2+3)/2
=(5+4√2)/2