# How do you simplify and find the restrictions for (3b)/(b(b + 9))?

Apr 27, 2017

See the solution process below:

#### Explanation:

To simplify this expression cancel the common term in the numerator and denominator:

$\frac{3 b}{b \left(b + 9\right)} = \frac{3 \textcolor{red}{\cancel{\textcolor{b l a c k}{b}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{b}}} \left(b + 9\right)} = \frac{3}{b + 9}$

To find the restrictions we need to use the original form of the expression. Because we cannot divide by $0$ we must solve for:

$b \left(b + 9\right) = 0$

To solve this we solve each term for 0:

1)

$b = 0$

2)

$b + 9 = 0$

$b + 9 - \textcolor{red}{9} = 0 - \textcolor{red}{9}$

$b + 0 = - 9$

$b = - 9$

The restrictions are:

$b \ne 0$ and $b \ne - 9$