已知a⼀b=c⼀d(b+-d不=0),求证:(a+c)⼀(a-c)=(b+d)⼀(b-d).

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2025-03-03 06:04:36
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回答1:

a/b=c/d ad=bc

(a+c)/(a-c)-(b+d)/(b-d)
=[(a+c)(b-d)-(b+d)(a-c)]/(a-c)(b-d)
=[ab-ad+bc-cd-ab+bc-ad+cd]/(a-c)(b-d)
=(2bc-2ad)/(a-c)(b-d)
=0

(a+c)/(a-c)=(b+d)/(b-d)