(1+1/16+1/17+1/18)x(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)x(1/16+1/17+1/18)怎么算

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(1+1/16+1/17+1/18)x(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)x(1/16+1/17+1/18)怎么算
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(1+1/16+1/17+1/18)x(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)x(1/16+1/17+1/18)怎么算
(1+1/16+1/17+1/18)x(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)x(1/16+1/17+1/18)怎么算

(1+1/16+1/17+1/18)x(1/16+1/17+1/18+1/19)-(1+1/16+1/17+1/18+1/19)x(1/16+1/17+1/18)怎么算
设a=1+1/16+1/17+1/18
b=1/16+1/17+1/18
则原式=a×(b+1/19)-(a+1/19)×b
=1/19×(a-b)
=1/19×1
=1/19

为了更直观 设1/16+1/17+1/18=A
原式化简为=(1+A) x (A+1/19)-(1+A+1/19) x A
=(1+A) x (A+1/19)-[A+A*(A+1/19)]
=(1+A) x (A+1/19)-A*(A+1/19)-A
=(A+1/19)+A*(A+1/19)-A*(A+1/19)-A
=(A+1/19)-A
=A+1/19-A
=1/19

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