foundation knowlege
2010-05-29 9:50 am
simplift (x-1)/(x+1-(3x+1)^0.5) and rationize the denominator of the answer.
回答 (1)
2010-05-29 4:29 pm
✔ 最佳答案
(x - 1)/[ (x + 1) - sqrt ( 3x + 1)]= (x - 1)[(x + 1) + sqrt ( 3x + 1)]/[(x + 1) + sqrt ( 3x + 1)][( x + 1) - sqrt (3x + 1)]
= (x - 1)[(x + 1) + sqrt (3x + 1)]/[(x + 1)^2 - ( 3x + 1)]
= (x - 1)[(x + 1) + sqrt (3x + 1)]/(x^2 + 2x + 1 - 3x - 1)
= (x - 1)[x + 1 + sqrt (3x + 1)/[x(x - 1)]
= [x + 1 + sqrt ( 3x + 1)]/x
2010-05-29 08:32:56 補充：
Remark: The key is to rationalize the expression by multiplying both the numerator and the denominator by x + 1 + sqrt ( 3x + 1).
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