abc为正数,a+b>c 证a/(a+1)+b/(b+1)>c/(c+1)
问题描述：
abc为正数,a+b>c 证a/(a+1)+b/(b+1)>c/(c+1)
答
构造函数:f(x)=x/(x+1)则；f(x)=x/(x+1)=[(x+1)-1]/(x+1)=1-[1/(x+1)]由于1/(x+1)在 (0,正无穷)上单调递减则:-[1/(x+1)]在 (0,正无穷)上单调递增则:f(x)=x/(x+1)在 (0,正无穷)上单调递增由于：a+b>c 且abc为正数则：...