Question

1.根号2+根号5-根号3/2*根号30-6*根号2+4*根号3 2.+除以 3.++……+

Answer 1

（1）
由于
2*根号30-6*根号2+4*根号3
=根号24*(根号2+根号5-根号3)
那么
根号2+根号5-根号3/2*根号30-6*根号2+4*根号3
=（根号2+根号5-根号3）/[根号24*(根号2+根号5-根号3)]
=1/根号24
=根号6/12
（2）
2x-6/x^2-9
=2（x-3）/[(x-3)(x+3)]
=2/(x+3)
x^2+2x+1/x^2+x-6
=(x+1)^2/[(x-2)(x+3)]
那么式子的后半部分为：
除以
=(x+1)^2*(x-2)/[(x+1)(x-2)(x-3)]
=(x+1)/(x+3)
+除以
=2/(x+3)+(x+1)/(x+3)
=(x+3)/(x+3)
=1
(3)
先考虑一个通式
1/[(n+1)*根号n+n*根号(n+1)]
=1/{根号[n*(n+1)]*[根号(n+1)+根号n]}
=[根号(n+1)-根号n]/根号[n*(n+1)]
=1/根号n-1/根号(n+1)
那么
++……+
=1/根号1-1/根号2+1/根号2-1/根号3+.+1/根号99-1/根号100
=1/根号1-1/根号100
=1-1/10
=9/10