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Um, hi. Small problem here. Make U the subject in:S= U*V / U + V (this being a fraction). Thanks.

 Mar 4, 2015

Best Answer 

 #2
avatar+22196 
+5

Make U the subject in:S= U*V / U + V (this being a fraction).

$$\small{\text{$
S= \dfrac{ U\cdot V } { U + V }
$}}\\\\
\small{\text{$
\dfrac{1}{S}= \dfrac{ U + V } { U\cdot V }
$}}\\\\
\small{\text{$
\dfrac{1}{S}= \dfrac{ U } { U\cdot V } + \dfrac{ V } { U\cdot V }
$}}\\\\
\boxed{\small{\text{$
\dfrac{1}{S}= \dfrac{ 1 } { V } + \dfrac{ 1 } { U }
$}}}\\\\
\small{\text{$
\dfrac{1}{U}= \dfrac{ 1 } { S } - \dfrac{ 1 } { V }
$}}\\\\
\small{\text{$
\dfrac{1}{U}= \dfrac{ V-S } { V\cdot S }
$}}\\\\
\boxed{
\small{\text{$
U= \dfrac{ V\cdot S } { V-S }
$}}}$$

.
 Mar 5, 2015
 #1
avatar+27852 
+5

$$S=\frac{U\times V}{U+V}$$

 

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:

 

$$U=-\frac{S\times V}{S-V}$$

.

 Mar 4, 2015
 #2
avatar+22196 
+5
Best Answer

Make U the subject in:S= U*V / U + V (this being a fraction).

$$\small{\text{$
S= \dfrac{ U\cdot V } { U + V }
$}}\\\\
\small{\text{$
\dfrac{1}{S}= \dfrac{ U + V } { U\cdot V }
$}}\\\\
\small{\text{$
\dfrac{1}{S}= \dfrac{ U } { U\cdot V } + \dfrac{ V } { U\cdot V }
$}}\\\\
\boxed{\small{\text{$
\dfrac{1}{S}= \dfrac{ 1 } { V } + \dfrac{ 1 } { U }
$}}}\\\\
\small{\text{$
\dfrac{1}{U}= \dfrac{ 1 } { S } - \dfrac{ 1 } { V }
$}}\\\\
\small{\text{$
\dfrac{1}{U}= \dfrac{ V-S } { V\cdot S }
$}}\\\\
\boxed{
\small{\text{$
U= \dfrac{ V\cdot S } { V-S }
$}}}$$

heureka Mar 5, 2015

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