Um, hi. Small problem here. Make U the subject in:S= U*V / U + V (this being a fraction). Thanks.
Make U the subject in:S= U*V / U + V (this being a fraction).
$$\small{\text{$
S= \dfrac{ U\cdot V } { U + V }
$}}\\\\
\small{\text{$
\dfrac{1}{S}= \dfrac{ U + V } { U\cdot V }
$}}\\\\
\small{\text{$
\dfrac{1}{S}= \dfrac{ U } { U\cdot V } + \dfrac{ V } { U\cdot V }
$}}\\\\
\boxed{\small{\text{$
\dfrac{1}{S}= \dfrac{ 1 } { V } + \dfrac{ 1 } { U }
$}}}\\\\
\small{\text{$
\dfrac{1}{U}= \dfrac{ 1 } { S } - \dfrac{ 1 } { V }
$}}\\\\
\small{\text{$
\dfrac{1}{U}= \dfrac{ V-S } { V\cdot S }
$}}\\\\
\boxed{
\small{\text{$
U= \dfrac{ V\cdot S } { V-S }
$}}}$$
$$S=\frac{U\times V}{U+V}$$
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:
$$U=-\frac{S\times V}{S-V}$$
.
.Make U the subject in:S= U*V / U + V (this being a fraction).
$$\small{\text{$
S= \dfrac{ U\cdot V } { U + V }
$}}\\\\
\small{\text{$
\dfrac{1}{S}= \dfrac{ U + V } { U\cdot V }
$}}\\\\
\small{\text{$
\dfrac{1}{S}= \dfrac{ U } { U\cdot V } + \dfrac{ V } { U\cdot V }
$}}\\\\
\boxed{\small{\text{$
\dfrac{1}{S}= \dfrac{ 1 } { V } + \dfrac{ 1 } { U }
$}}}\\\\
\small{\text{$
\dfrac{1}{U}= \dfrac{ 1 } { S } - \dfrac{ 1 } { V }
$}}\\\\
\small{\text{$
\dfrac{1}{U}= \dfrac{ V-S } { V\cdot S }
$}}\\\\
\boxed{
\small{\text{$
U= \dfrac{ V\cdot S } { V-S }
$}}}$$