# Question #b8a65

Jun 20, 2016

The format of the question is not clear.
$b = \frac{3}{24} = \frac{1}{8} \text{ or } b = - \frac{20}{3} = - 6 \frac{2}{3}$

#### Explanation:

The format of the question is not clear.

It could be $\frac{3}{3 b} + 4 = \frac{2}{b} - 4 \text{ " or " } \frac{3}{3 b + 4} = \frac{2}{b - 4}$

In $\frac{3}{3 b} + 4 = \frac{2}{b} - 4 \text{ multiply by 3b to cancel the denominators}$

$\textcolor{red}{3 b} \times \frac{3}{3 b} + 4 \times \textcolor{red}{3 b} = \frac{2}{b} \times \textcolor{red}{3 b} - 4 \times \textcolor{red}{3 b}$

$\cancel{\textcolor{red}{3 b}} \times \frac{3}{\cancel{3 b}} + 4 \times \textcolor{red}{3 b} = \frac{2}{\cancel{b}} \times \textcolor{red}{3 \cancel{b}} - 4 \times \textcolor{red}{3 b}$

$3 + 12 b = 6 - 12 b$

$24 b = 3$

$b = \frac{3}{24} = \frac{1}{8}$

In $\frac{3}{3 b + 4} = \frac{2}{b - 4} \text{ }$ There is one fraction on each side of $\text{ }$the equal sign, so we can cross multiply.

$2 \left(3 b + 4\right) = 3 \left(b - 4\right)$

$6 b + 8 = 3 b - 12$

$3 b = - 20$

$b = - \frac{20}{3} = - 6 \frac{2}{3}$