Question

(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)

Answer 1

设 1/5+1/7+1/9+1/11 = a，1/7+1/9+1/11=b，则 a-b=1/5
a*(b+1/13)-(a+1/13)b
=ab+a*1/13-ab-b*1/13
=(a-b)/13
=1/5/13
=1/65

追问

能详细点吗？急急急急急急急！！！！！！！快点！！！！！！！！！！！！

追答

设 1/5+1/7+1/9+1/11 = a，1/7+1/9+1/11=b，则 a-b=1/5
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)
代入后
=a*(b+1/13)-(a+1/13)b
展开
=ab+a*1/13-ab-b*1/13
消项
=(a-b)/13
代入
=1/5/13
=1/65

Answer 2

令a=1/7+1/9+1/11
原式=(1/5+a)(a+1/13)-(1/5+a+1/13)a
=(1/5+a)a+(1/5+a)*1/13-(1/5+a)-1/13*a
=(1/5+a)*1/13-1/13*a
=1/65+1/13*a-1/13*a
=1/65