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

題目：

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

解答：

設 a/b=c/d = k
則 a = bk,c = dk
代入到所要證明的式子中
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
命題成立.