# How do you solve \frac { b } { b + 7} - 9= \frac { - 7} { b + 7}?

May 25, 2017

No solution

#### Explanation:

Multiply both sides by $b + 7$. Note that this means that $b \ne - 7$:

$\left(b + 7\right) \left(\frac{b}{b + 7} - 9\right) = \left(b + 7\right) \left(- \frac{7}{b + 7}\right)$

This becomes:

$b - 9 b - 63 = - 7$

Consolidate the $b$s:

$- 8 b - 63 = - 7$

Add $63$ to both sides:

$- 8 b - 63 + 63 = - 7 + 63$

This becomes:

$- 8 b = 56$

Divide both sides by $- 8$:

$\frac{- 8 b}{-} 8 = \frac{56}{-} 8$

This becomes:

$b = - 7$

However, don't forget about the initial condition. $b$ is not allowed to be $- 7$. So we have no solution.