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November 12th, 2011, 02:43 AM  #1 
Newbie Joined: Nov 2011 Posts: 2 Thanks: 0  to prove inequality
Suppose x > 1, then x/(x+1) < (x+1)/(x+2) this needs to be proven ^ I tried to go direct and I ended up with this x(x+1)(x+2)^2 < (x+1)^3(x+2) I don't know where to go to from there o.O I tried using induction to continue but it doesn't work... Thoughts? 
November 12th, 2011, 05:52 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: to prove inequality
x/(x + 1) < (x + 1)/(x + 2) x/(x + 1)  (x + 1)/(x + 2) < 0 (x² + 2x  x²  2x  1)/((x + 1)(x + 2)) < 0 1/((x + 1)(x + 2)) < 0. The denominator is a parabola that opens upward and has zeros 1 and 2 so the denominator is negative for 2 < x < 1, so the inequality x/(x + 1) < (x + 1)/(x + 2) is true for x > 1, x < 2. 
November 12th, 2011, 06:17 AM  #3 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: to prove inequality
Or For , true for and true for all x. Hence and 
November 12th, 2011, 08:07 AM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: to prove inequality Hello, jamesb1! Quote: [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color]  

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