题目
已知a/b=c/d,求证:(3a+2c)/(3a-2c)=(3b+2d)/(3b-2d)
提问时间:2020-09-26
答案
∵a/b=c/d,∴a/c=b/d,∴3a/(2c)=3b/(2d),∴3a/(2c)+1=3b/(2d)+1,
∴(3a+2c)/(2c)=(3b+2d)/(2d).······①
∵3a/(2c)=3b/(2d),∴3a/(2c)-1=3b/(2d)-1,
∴(3a-2c)/(2c)=(3b-2d)/(2d).······②
①÷②,得:(3a+2c)/(3a-2c)=(3b+2d)/(3b-2d).
∴(3a+2c)/(2c)=(3b+2d)/(2d).······①
∵3a/(2c)=3b/(2d),∴3a/(2c)-1=3b/(2d)-1,
∴(3a-2c)/(2c)=(3b-2d)/(2d).······②
①÷②,得:(3a+2c)/(3a-2c)=(3b+2d)/(3b-2d).
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