已知$x,y>0,dfrac{1}{x}+dfrac{2}{y}=1$,求$dfrac{1}{x+1}+dfrac{2}{y+1}$的最大值____
解答：令$a=dfrac{1}{x},b=dfrac{2}{y}$则$a,b>0,a+b=1$
$dfrac{1}{x+1}+dfrac{2}{y+1}=dfrac{a}{a+1}+dfrac{2b}{b+2}=3-(dfrac{1}{a+1}+dfrac{4}{b+2})le 3-dfrac{9}{a+b+3}=dfrac{3}{4}$
已知$x,y>0,dfrac{1}{x}+dfrac{2}{y}=1$,求$dfrac{1}{x+1}+dfrac{2}{y+1}$的最大值____
解答：令$a=dfrac{1}{x},b=dfrac{2}{y}$则$a,b>0,a+b=1$
$dfrac{1}{x+1}+dfrac{2}{y+1}=dfrac{a}{a+1}+dfrac{2b}{b+2}=3-(dfrac{1}{a+1}+dfrac{4}{b+2})le 3-dfrac{9}{a+b+3}=dfrac{3}{4}$