Comparing two fractionsI saw this problem from an elementary textbook:Let A = 2014 2015 + 2015 2016 and B = 2014 + 2015 2015 + 2016 Compare A and B.I know the answer is A &gt; B because A B &gt; 1.But I cannot find a precise way to explain it. Can anyone please help? Thank you.

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Comparing two fractionsI saw this problem from an elementary textbook:Let  A  =      2014    2015    +      2015    2016  and  B  =            2014      +      2015              2015      +      2016      Compare A and B.I know the answer is   A  &amp;gt;  B because      A    B    &amp;gt;  1.But I cannot find a precise way to explain it. Can anyone please help? Thank you.

frethi38 · Accepted Answer

Beside the general proofs given in answers  A  =      2014    2015    +      2015    2016    =            2014      +      1      −      1        2015    +            2015      +      1      −      1        2016    =  1  −      1    2015    +  1  −      1    2016    A  =  2  −      1    2015    −      1    2016    =  2  −  s  m  a  l      l    1    B  =            2014      +      2015              2015      +      2016        =            2014      +      1      −      1      +      2015      +      1      −      1              2015      +      2016        =            2015      −      1      +      2016      −      1              2015      +      2016        B  =  1  −      2          2015      +      2016        =  1  −  s  m  a  l      l    2

Dwllane4 · Accepted Answer

We are comparing       a    b    +      b    c   with             a      +      b              b      +      c             a    b    +      b    c    =            a      (                        b          +          c                b            )      +      b      (                        b          +          c                c            )              b      +      c       so we can compare the numerators.  a  (            b      +      c        b    )  =  a  (  1  +      c    b    )  &amp;gt;  aLikewise,  b  (            b      +      c        c    )  =  b  (  1  +      b    c    )  &amp;gt;  bTherefore,       a    b    +      b    c    =            a      (                        b          +          c                b            )      +      b      (                        b          +          c                c            )              b      +      c        &amp;gt;            a      +      b              b      +      c       so   A  &amp;gt;  B

Comparing two fractions I saw this problem from an elementary textbook: Let A =

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