(1\5+1\7+9\1+1\11)x(1\7+1\9+1\11+1\13)-(1\5+1\7+1\9+1\11+1\13)x(1\7+1\9+1\11)

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(1\5+1\7+9\1+1\11)x(1\7+1\9+1\11+1\13)-(1\5+1\7+1\9+1\11+1\13)x(1\7+1\9+1\11)
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(1\5+1\7+9\1+1\11)x(1\7+1\9+1\11+1\13)-(1\5+1\7+1\9+1\11+1\13)x(1\7+1\9+1\11)
(1\5+1\7+9\1+1\11)x(1\7+1\9+1\11+1\13)-(1\5+1\7+1\9+1\11+1\13)x(1\7+1\9+1\11)

(1\5+1\7+9\1+1\11)x(1\7+1\9+1\11+1\13)-(1\5+1\7+1\9+1\11+1\13)x(1\7+1\9+1\11)
令a=1\5+1\7+9\1+1\11
b=1\7+1\9+1\11+1\13
则原式=ab-(a+1/13)(b-1/13)
=ab-ab+a/13-b/13+1/169
=(a-b)/13+1/169
=(1/5-1/13)/13+1/169
=1/65-1/169+1/169
=1/65

令x=(1\5+1\7+9\1+1\11)
y=(1\7+1\9+1\11+1\13)
原式=xy-(x+1/13)(y-1/13)
=-y/13+x/13+1/169
=8/845+1/169=13/845=1/65

原式=(1/5+1/7+1/9+1/11)×[(1/7+1/9+1/11)+1/13]-[(1/5+1/7+1/9+1/11)+1/13]×(1/7+1/9+1/11)=(1\5+1\7+9\1+1\11)x(1\7+1\9+1\11)+(1\5+1\7+9\1+1\11)x1/13-(1\5+1\7+1\9+1\11)x(1\7+1\9+1\11)-1\13x(1\7+1\9+1\11)=1/13×(1/5-1)=-4/65

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