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If S and T are non-zero numbers and 1/S+1/T=S+T , which of the following is necessarily true? (A) ST=1 (B) S+T=1 (C) 1/S=T (D) S/T=1 (E) none of the above

Please help me understand right answer.I marked A, but it's wrong.

1/S +1/T = (T+S)/TS = S + T => S + T = ST(S + T) So we have ST = 1 and S+T =0. We also get 1/S =T

now taking the options one by one --- A) ST=1 ----- possible (B) S+T=1-----not possible (C) 1/S=T-----possible (D) S/T=1---need to check (E) none of the above

now if S =3 and T = -3 then ST is not equal to 1 so option A and D are out 1/S is not equal to T and S/T is also not equal to 1 so option C and B are also out