已知:a/b=c/d,求证:(2a+3b)/(a+b)=(2c+3d)/(c+d)

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已知:a/b=c/d,求证:(2a+3b)/(a+b)=(2c+3d)/(c+d)

已知:a/b=c/d,求证:(2a+3b)/(a+b)=(2c+3d)/(c+d)
已知:a/b=c/d,求证:(2a+3b)/(a+b)=(2c+3d)/(c+d)

已知:a/b=c/d,求证:(2a+3b)/(a+b)=(2c+3d)/(c+d)
设 a/b=c/d = k
则 a = bk,c = dk
代入到所要证明的式子中
左 =(2a+3b)/(a+b)
= (2bk + 3b)/(bk +b)
= (2k+3)/(k+1)
右=(2c+3d)/(c+d)
= (2dk + 3d)/(dk + d)
= (2k+3)/(k+1)
所以 左 = 右
命题成立.

设a/b=c/d=k
则a=bk
c=dk
:(2a+3b)/(a+b)
=(2bk+3b)/(bk+b)
=(2k+3)/(k+1)
(2c+3d)/(c+d)
=(2dk+3d)/(dk+d)
=(2k+3)/(k+1)
则:(2a+3b)/(a+b)=(2c+3d)/(c+d)