# If c=(2ab)/(a+b) then b=?

Jul 14, 2016

color(blue)(b=(ac)/(2a-c)

#### Explanation:

$c = \frac{2 a b}{a + b}$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow c \left(a + b\right) = 2 a b$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow a c = 2 a b - c b$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow a c = \left(2 a - c\right) b$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow b = \frac{a c}{2 a - c}$

Note: in order to obtain a meaningful result we have needed to assume (for example) $2 a - c \ne 0$