$$S=\frac{U\times V}{U+V}$$
Multiply both sides by U + V:
$$S\times (U+V)=U\times V$$
Expand the left-hand side:
$$S\times U + S\times V = U\times V$$
Subtract U*V and S*V from both sides:
$$S\times U-U\times V=-S\times V$$
Factor out U on the left-hand side:
$$U\times (S-V)=-S\times V$$
Divide both sides by S - V:
$$U=-\frac{S\times V}{S-V}$$
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