If 1/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c 1 0; abc 1 0, then what is the value of ( a
+ b ) ( b + c ) ( c + a )?  Choose one
A) Equal to 0 B) Greater than 0 C) Less than 0 D) Less than 1 E) Cannot be determined
1/a+1/b+1/c=1/(a+b+c)   or (bc+ac+ab)/(abc)=1/(a+b+c)   or (ab+bc+ac)(a+b+c)=abc   or abc+(a^2)c+(a^2)b+(b^2)c+abc+(b^2)a+(c^2)b+(c^2)a+abc=abc   or 2abc+(a^2)c+(a^2)b+(b^2)c+(b^2)a+(c^2)b+(c^2)a=0   also,   ( a+ b ) ( b + c ) ( c + a )=2abc+(a^2)c+(a^2)b+(b^2)c+(b^2)a+(c^2)b+(c^2)a   or ( a+ b ) ( b + c ) ( c + a )=0   Equal to 0NSWER:Equal to 0
<result>A</result>
If 1/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c 1 0; abc 1 0, then what is the value of ( a
+ b ) ( b + c ) ( c + a )?