[tex]P=\frac{a+b+c}{abc}+\frac{1}{1-2(ab+bc+ca)}=\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{1-2(ab+bc+ca)}\geq \frac{9}{ab+bc+ca}+\frac{1}{1-2(ab+bc+ca)}[/tex]
[tex]P\geq \frac{7}{ab+bc+ca}+\frac{1}{ab+bc+ca}+\frac{1}{ab+bc+ca}+\frac{1}{1-2(ab+bc+ca)}\geq \frac{21}{(a+b+c)^2}+\frac{9}{1}=30[/tex]