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Algebra Level 3

Let

$a=\frac{2013}{2012*2014}$

$b=\frac{2014}{2013*2015}$ and

$c=\frac{1}{2014}$

Then arrange $a,b,c$ in ascending order.

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2 solutions

Sandeep Rathod
Nov 11, 2014

$a = \frac{ 2012 + 1}{2012.2014}$

$a = c + \frac{1}{2012.2014}$

$b = \frac{2014}{(2014 - 1)(2014 + 1)} = \frac{2014}{2014^{2} - 1}$

$b = \frac{1}{ 2014 - \frac{1}{2014}}$ ( b will be always greater than c)

Thus $c < b < a$

You showed that a and b are greater than c...but where did you show that a>b. It is the same methodology as for b and c Just figured it out

Greg Grapsas - 2 years, 1 month ago

Abdelrahman Sabri
Oct 13, 2014

2012x2014=(2013-1)(2013+1)=(2013^2)-1 and 2013x2015=(2014-1)(2014+1)=(2014^2)-1. a=2013/((2013^2)-1) , b=2014/((2014^2)-1) , and a=1/(2013-(1/2013)) , b=1/(2014-(1/2014)) , obviously 2014>2014-(1/2014)>2013-(1/2013) then c<b<a

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