We can find a common denominator on the left side:

\(\frac{1}{S} + \frac{1}{T} = S + T \\

\frac{T}{ST} + \frac{S}{ST} = S+T \\

\frac{S + T}{ST} = S + T\)

Now, if \(S + T \neq 0\), we can divide both sides by \(S + T\) to get:

\(\frac{1}{ST} = 1 \\

ST = 1\)

So if \(S + T \neq 0\), then \(ST = 1\) must be true. However, we can't be sure that \(S + T \neq 0\) is true, as you can see by plugging in, say, S = 2 and T = -2. So the answer is E.

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