实数a,b满足ab不等于0,且使得a/(l+a)+b/(l+b)=(a+b)/(1+a+b),求a+b的值
问题描述:
实数a,b满足ab不等于0,且使得a/(l+a)+b/(l+b)=(a+b)/(1+a+b),求a+b的值
答
等式左边通分,得:(a+b+2ab)/(1+a+b+ab)=(a+b)/(1+a+b)
设a+b=u,代入得:(u+2ab)/(u+ab+1)=u/(u+1)
两边乘以:(u+1)(u+ab+1),整理得:abu=-2ab,因为ab>