How to simplify this expression?
2017-09-12 8:56 pm
(√(x-1)/(√(x+1)-√x))+(√(x+1)/(√(x-1)+√x)), where x>1. I need the steps. The answer is √(x^2-x)+√(x^2+x).
回答 (2)
2017-09-13 7:33 am
✔ 最佳答案
SolA=√(x－1)，B=√x，C=√(x+1)
AB=√(x^2－x)
BC=√(x^2+x)
C^2－B^2=1
A^2－B^2=－1
√(x－1)/(√(x+1)－√x))+(√(x+1)/(√(x－1)+√x))
=A/(C－B)+C/(A+B)
=(AC+AB)/(C^2－B^2)+(AC－BC)/(A^2－B^2)
=AC+AB－AC+BC
=AB+BC
=√(x^2－x)+√(x^2+x)
2017-09-12 11:11 pm
{(√(x-1))(√(x+1)+√x)/(√(x+1)-√x)(√(x+1)+√x)}+(√(x+1)(√(x-1)-√x)/(√(x-1)+√x)(√(x-1)-√x)
收錄日期: 2021-04-18 17:54:50
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170912125648AAZOr1S