根号下X+根号下1/X=2,那么根号下X/(X^2+3X+1)-根号下X/(X^2+9X+1)的值等于

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根号下X+根号下1/X=2,那么根号下X/(X^2+3X+1)-根号下X/(X^2+9X+1)的值等于
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根号下X+根号下1/X=2,那么根号下X/(X^2+3X+1)-根号下X/(X^2+9X+1)的值等于
根号下X+根号下1/X=2,那么根号下X/(X^2+3X+1)-根号下X/(X^2+9X+1)的值等于

根号下X+根号下1/X=2,那么根号下X/(X^2+3X+1)-根号下X/(X^2+9X+1)的值等于

√x+√(1/x)=2 ===> [√x+√(1/x)]^2=4 ===> x+2+(1/x)=4
===> x+(1/x)=2
所以原式=√[x/(x^2+3x+1)]-[√x/(x^2+9x+1)]
=√1/[x+3+(1/x)]-√1/[x+9+(1/x)]
=√[1/(2+3)]-√[1/(2+9)]
=(√5/5)-(√11/11).