(1)/(1+a+b^(-1))+(1)/(1+b+c^(-1))+(1)/(1+c+a^(-1))

If abc=1, show that (1)/(1+a+b^(-1))+(1)/(1+b+c)+(1)/(1+c+a^(-1))=1

Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

If a ((1)/(b) + (1)/(c )), b ((1)/(c )+ (1)/(a)), c ((1)/(a) + (1)/(b)) are in A.P., then

Let a , b , c ne three distinct non-zero real numbers satisfying the system of equation (1)/(a)+(1)/(a-1)+(1)/(a-2)=1 , (1)/(b)+(1)/(b-1)+(1)/(b-2)=1 , (1)/(c )+(1)/(c-1)+(1)/(c-2)=1 . Then abc=

If a, b, c are in A.P. then prove that the following are also in A.P:(iii) (1)/(a)((1)/(b)+(1)/(c )),(1)/(b)((1)/(c )+(1)/(a)),(1)/(c )((1)/(a)+(1)/(b)) are in A.P