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

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

Guest Mar 4, 2015

#2
+19207
+5

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

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

heureka  Mar 5, 2015
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#1
+26642
+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:

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

.

Alan  Mar 4, 2015
#2
+19207
+5
$$\small{\text{ S= \dfrac{ U\cdot V } { U + V } }}\\\\ \small{\text{ \dfrac{1}{S}= \dfrac{ U + V } { U\cdot V } }}\\\\ \small{\text{ \dfrac{1}{S}= \dfrac{ U } { U\cdot V } + \dfrac{ V } { U\cdot V } }}\\\\ \boxed{\small{\text{ \dfrac{1}{S}= \dfrac{ 1 } { V } + \dfrac{ 1 } { U } }}}\\\\ \small{\text{ \dfrac{1}{U}= \dfrac{ 1 } { S } - \dfrac{ 1 } { V } }}\\\\ \small{\text{ \dfrac{1}{U}= \dfrac{ V-S } { V\cdot S } }}\\\\ \boxed{ \small{\text{ U= \dfrac{ V\cdot S } { V-S } }}}$$