(1)a/c和b/c
(a/c):(b/c)=(a/c)*(c/b)=a:b
即(a/c):(b/c)=a:b
(2)b/a和d/c
b/a=1/(a/b)=1/(c/d)=d/c
即b/a=d/c
(即都倒过来仍相等)
(3)(a+b)/b和(c+d)/d
(a+b)/b=a/b+b/b=a/b+1=c/d+1=c/d+d/d=(c+d)/d
即(a+b)/b=(c+d)/d
(同理(a+b)/a=(c+d)/c(为下一题做准备))
(4)(a+b)/(a-b)和(c+d)/(c-d) (a≠b,c≠d)
因为(a+b)/b=(c+d)/d及(a+b)/a=(c+d)/c
根据(2)的结论,
所以有b/(a+b)=d/(c+d)和a/(a+b)=c/(c+d)
两个等式相减
所以a/(a+b)-b/(a+b)=c/(c+d)-d/(c+d)
即(a-b)/(a+b)=(c-d)/(c+d)
根据(2)的结论,
有(a+b)/(a-b)=(c+d)/(c-d)