(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)
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设1/2+1/3+1/4=x
1/2+1/3+1/4+1/5=y
(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)
=（1+x)y-(1+y)x
=y+xy-x-xy
=y-x
=1/5
1/2+1/3+1/4+1/5=y
(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)
=（1+x)y-(1+y)x
=y+xy-x-xy
=y-x
=1/5
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因式分解
(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -[1 x(1/2+1/3+1/4)+(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)]
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -1 x(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)
=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)
=1/5
(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -[1 x(1/2+1/3+1/4)+(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)]
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -1 x(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)
=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)
=1/5
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设1/2+1/3+1/4=x
1/2+1/3+1/4+1/5=y
(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)
=（1+x)y-(1+y)x
=y+xy-x-xy
=y-x
=1/5
1/2+1/3+1/4+1/5=y
(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)
=（1+x)y-(1+y)x
=y+xy-x-xy
=y-x
=1/5
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