`(b+c)/(bc)(b+c-a)+(c+a)/(ca)(c+a-b)+(a+b)/(ab)(a+b-c)`

If a,b,c are in AP, show that (a(b+c))/(bc) , (b (c+a))/(ca), (c(a+b))/(ab) , are also in AP.

If bc + ab + ca = abc, then the value of (b+c)/(bc(1-a))+(a+c)/(ac(1-b))+(a+b)/(ab(1-c)) is

If ab + bc + ca = 0, then find the value of (b)/((a+b)(b+c))+(c)/((a+c)(c+b))+(a)/((a+b)(c+a))

If a^(2) +b^(2) +c^(2) = ab + bc + ca then ((a+b)/(c ) + (b+c)/(a) + (c+a)/(b)) ((c )/(a+b) + (b)/(a+c) + (c )/(a+b)) =?

The expression (a-b)^(3)+(b-c)^(3)+(c-a)^(3) can be factorized as (a)(a-b)(b-c)(c-a)(b)3(a-b)(b-c)(c-a)(c)-3(a-b)(b-c)(c-a)(d)(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)

Ifa+b+c=0, findthevalue ((b+c)^(2))/(bc)+((c+a)^(2))/(ca)+((a+b)^(2))/(ab)

If a,b,are positive then which of the following holds good?(A) b^(c)-2+c^(2)a^(2)+a^(2)b^(2)>=abc(a+b+c)(B)(bc)/(a)+(ca)/(b)+(ab)/(c)>=a+b+c((C)(bc)/(a^(3))+c(a)/(b^(3))+a(b)/(c^(3))>=(1)/(a)+(1)/(b)+(1)/(c)(D)(1)/(a)+(1)/(b)+(1)/(c)>=(1)/(sqrt(bc))+(1)/(sqrt(ca))+(1)/(sqrt(ab)))

If a*b*c means (a+b)/(c) for all numbers except 0, then (a*b*c)*a*b is equal to (a)0(b)1 (c) (a+b+c)/(ab) (d) (a+b+ac)/(bc) (e) (ab+bc+ca)/(a+b+c)