# Practice! #3

Algebra Level 5

$\dfrac{a^{3}}{b+c+d}+\dfrac{b^{3}}{a+c+d}+\dfrac{c^{3}}{a+b+d}+\dfrac{d^{3}}{a+b+c}$ If $$ab+bc+cd+da=1$$ and $$a,b,c,d$$ are non-negative real number and the expression above can be expressed as $$\dfrac{m}{n}$$ and $$m,n$$ are coprime positive integer. What is the minimum value of $$m+n$$?

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