(1+根2/根5+根3)+(1-根2/根5-根3)=根5-根6

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(1+根2/根5+根3)+(1-根2/根5-根3)=根5-根6
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(1+根2/根5+根3)+(1-根2/根5-根3)=根5-根6
(1+根2/根5+根3)+(1-根2/根5-根3)=根5-根6

(1+根2/根5+根3)+(1-根2/根5-根3)=根5-根6
(1+√2)/(√5+√3)+(1-√2)/(√5-√3)
=(1+√2)(√5-√3)/(5-3)+(1-√2)(√5+√3)/(5-3)
=(2√5-2√6)/2
=√5-√6

通分得
原式=[(1+√2)(√5-√3)+(1-√2)(√5+√3)]/[(√5+√3)(√5-√3)]
=(√5-√3+√10-√6+√5+√3-√10-√6)/2
=√5-√6