Question 775345
<pre>
{{{(a/(b+c)) +(b/(a+c)) +(c/(b+a))}}}{{{""=""}}}{{{(a^3+a^2b+a^2c+ab^2+3abc+ac^2+b^3+b^2 c+bc^2+c^3)/(a^2b+a^2c+ab^2+2abc+ac^2+b^2c+bc^2)}}}{{{""=""}}}{{{1+(a^3+abc+b^3+c^3)/(a^2b+a^2c+ab^2+2abc+ac^2+b^2c+bc^2)}}}

and if you reduce any one of the letters, you will reduce the numerator more
that you've reduced the denominator, so the maximum value of the fraction is
when all three sides are equal: 

When a=b=c

{{{(a/(a+a)) +(a/(a+a)) +(a/(a+a))}}} =

{{{a/(2a)+a/(2a)+a/(2a)}}} =

{{{1/2+1/2+1/2}}}

{{{3/2}}}

Edwin</pre>