If `a=-10,b=1` and `c=1` , Show that ` a -: (b+c) != (a -:b) + (a-:c)`

Show that |1a b_c1b c+a1c a+b|=0

If (b+c)^(-1), (c+a)^(-1), (a+b)^(-1) are in A.P. then show that (a)/(b+c) , (b)/(c+a) , (c)/(a+b) are also in A.P.

If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P., then show that : b=(2ac)/(a+c) and b/d=(3a-c)/(a+c) .

If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a b) are in A.P.

If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)<1/2(a+b+c)

If a,b,c are in G.P., show that 1/(a+b),1/(2b),1/(b+c) are in A.P.

If a^(2)/(b + c) = b^(2)/(c +a) = c^(2)/(a + b) = 1 , then show that 1/(1+a) + 1/(1 + b) + 1/(1+c) = 1 .

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