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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 (x� + 2x - x� - 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
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Re: to prove inequality

Hello, jamesb1!

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