<s>[INST] Non Linear Algebraic Equation If$$ abc = 4(4+a+b+c) , find $$ $$1/(2+a) +1/(2+b) + 1/(2+c).$$
My approach; put $$a=b=c=4 $$ and we are done. Looking at the symmetry of the equation, i think it is the only value that will satisfy the given equation or if otherwise, it is too difficult to get it by hit and trail.
Any better solution will be appreciated. 
Thank you.
 [/INST] This is basically an exercise in simplification.
Rewrite the target expression as (after adding and simplifying): $$\frac{12+4(a+b+c)+ab+bc+ca}{8+4(a+b+c)+2(ab+bc+ca)+abc}=\frac{4(4+a+b+c)+ab+bc+ca-4}{4(4+a+b+c)+2(ab+bc+ca)+abc-8}.$$
Substituting using the given relationship results in $$\frac{abc+ ab+bc+ca-4}{2abc+2(ab+bc+ca)-8}=\frac{1}{2}.$$
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