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

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

Prove that (a+b)^(-1)(a^(-1)+b^(-1))=(1)/(ab)

Prove that :(a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^(2))/(b^(2)-a^(2))

Prove that : (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(b^2-a^2)

Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(b^2-a^2)

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

Prove that: a^(-1)/(a^-1 +b^-1)+a^-1/(a^-1-b^-1)=(2b^2)/(b^2-a^2)

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

Prove that (i) (a^(-1))/(a^(-1) + b^(-1)) + (a^(-1))/(a^(-1)-b^(-1)) = (2b^(2))/(b^(2) -a^(2)) (ii) (1)/(1+x^(a-b)) + (1)/(1+x^(b-a)) = 1

Prove that, "tan"^(-1)(a)/(b)-"tan"^(-1)((a-b)/(a+b))=(pi)/(4) .