# Question #3127e

Jan 10, 2017

$b = \frac{c d - a c}{a - d - a c}$

#### Explanation:

The problem is that there is more than one term with $b$.

Remove the brackets:

$a \left(b + c\right) - d \left(b + c\right) = a b c$

$\textcolor{b l u e}{a b} + a c \textcolor{b l u e}{- b d} - c d = \textcolor{b l u e}{a b c} \text{ } \leftarrow$move all 'b' terms to one side

$\textcolor{b l u e}{a b - b d - a b c} = - a c + c d \text{ } \leftarrow$ Factor out 'b'

$\textcolor{red}{b} \left(a - d - a c\right) = - a c + c d \text{ } \leftarrow$ there is now only one 'b'

$\textcolor{red}{b} = \frac{c d - a c}{a - d - a c} \text{ } \leftarrow$ divide to isolate 'b'