Question

简便计算，急急急急急急急急急！！！！快快。

(1/11加1/21加1/31加1/41)×(1/21加1/31加1/41加1/51)-(1/11加1/21加1/31加1/41加1/51)×(1/21加1/31加1/41)

Answer 1

将1/21+1/31+1/41看成一个整体设为X，则原式=（1/11+x）(x+1/51)-(1/11+x+1/51)x=(1/11)x+x^2+(1/11)(1/51)+(1/51)x-(1/11)x-x^2-(1/51)x=(1/11)(1/51)=1/561。

Answer 2

(1/11+1/21+1/31+1/41)*(1/21+1/31+1/41+1/51)-(1/11+1/21+1/31+1/41+1/51)*(1/21+1/31+1/41)

=(1/11+1/21+1/31+1/41)*【(1/21+1/31+1/41)+1/51】-【(1/11+1/21+1/31+1/41）+1/51】*(1/21+1/31+1/41)
==(1/11+1/21+1/31+1/41)*(1/21+1/31+1/41)+(1/11+1/21+1/31+1/41)*1/51-(1/11+1/21+1/31+1/41）*(1/21+1/31+1/41)-1/51*(1/21+1/31+1/41)
=(1/11+1/21+1/31+1/41)*1/51-1/51*(1/21+1/31+1/41)
=【(1/11+1/21+1/31）+1/41】*1/51-1/51*(1/21+1/31+1/41)

=(1/11+1/21+1/31）*1/51+1/41*1/51-1/51*(1/21+1/31+1/41)
=1/41*1/51
=1/2091

Answer 3

为了方便设M(1/11加1/21加1/31加1/41）
(1/11加1/21加1/31加1/41)×(1/21加1/31加1/41加1/51)-(1/11加1/21加1/31加1/41加1/51)×(1/21加1/31加1/41)
=M(M-1/11+1/51)-(M+1/51)X(M-1/11)
=1/51x(-1/11)
= -1/605
该抵消的都抵消了！