Question

化简1/(根号2-1)+2/(根号3+1)的结果是？

化简1/(根号2-1)+2/(根号3+1)的结果是？要过程。

Answer 1

1/(根号2-1)+2/(根号3+1)

=（√2+1）/[(√2+1)(√2-1)]+2×(√3-1)/[(√3+1)(√3-1)]
=(√2+1)/(2-1)+2×(√3-1)/(3-1)
=√2+1+√3-1
=√2+√3

追问

√2+1）/[(√2+1)(√2-1)]+2×(√3-1)/[(√3+1)(√3-1)]这一步没大搞懂，求解释，如果明白，选你为最佳答案。

追答

分母有理化
1/(根号2-1)分子分母同乘以(√2-1)

2/(根号3+1)分子分母同乘以(√3-1)

Answer 2

1/(√2-1)+2/(√3+1)

=(√2+1)/[(√2-1)(√2+1)]+2(√3-1)/[(√3+1)(√3-1)]
=√2+1+√3-1
=√2+√3

Answer 3

1/(√2-1)+2/(√3+1)
=(√2+1)/(2-1)+2(√3-1)/(3-1)
=√2+1+√3-1
=√2+√3

Answer 4

解答：
1/√2 - 1 + 2/√3 +1
=√2+1/(√2 - 1)(√2+1) + 2(√3-1)/(√3 +1)(√3-1)
=√2+1/2-1 + 2√3-2/3-1
=√2+1/1 + 2√3-2/2
=√2+1 + √3-1/1
=√2+1+√3-1
=√2+√3 .

Answer 5

解：
1/(根号2-1)+2/(根号3+1)

=(根号2-1)(根号2+1)/(根号2-1)+(根号3+1)(根号3-1)/(根号3+1)
=根号2+1+根号3-1=根号2+根号3
希望我的回答可以帮助你

Answer 6

√2+√3 ，分母有理化，乘以共轭根式