(a^2-bc)(b-abc)=(b^2-ac)(a-abc)
<=>a^2.b-a^3.bc-b^2.c+a.b^2.c^2=a.b^2-a.b^3.c-a^2.c+a^2.b.c^2
<=>a^2.b-a.b^2+a^2.c-b^2.c=+a^3.bc-a.b^3.c+a^2.b.c^2-a.b^2.c^2
<=>ab(a-b)+c(a-b)(a+b)=abc(a^2-b^2)+abc^2(a-b)
<=>(a-b)(ab+ac+bc)=abc(a-b)(a+b+c)
<=>ab+ac+bc=abc(a+b+c)
<=>(ab+ac+bc)/abc=a+b+c
<=>ab/abc+ac/abc+bc/abc=a+b+c
<=>1/a+1/b+1/c=a+b+c