If `a,b,c` are in H.P., show that `(a-b)/(b-c)=a/c`

If a,b,c are in H.P. show that a/(b+c),b/(c+a),c/(a+b) are also in H.P.

If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.P. .

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.P. .

If a, b, c are in H.P., prove that (a)/(b+c), (b)/(c+a) and (c )/(a+b) are also in H.P.

If a, b, c are in H.P., prove that, (a)/(a-b) = (a+c)/(a-c)

If a, b, c are in H.P., prove that, (a)/(b+c-a), (b)/(c+a-b), (c )/(a+b-c) are in H.P.

If a,b,c are in H.P.,then prove that (a)/(b+c-a),(b)/(a+b-c),(c)/(a+b-c) are in H.P.

If a,b,c are in H.P., then (b+a)/(b-a)+(b+c)/(b-c)