# How do you solve -\frac { 27} { w ^ { 2} - 9w + 8} = - \frac { 3w } { w - 1}?

Apr 28, 2017

$w = - 1 , 1 , 9$

#### Explanation:

First we can divide both sides by $- 1$ to remove the negative signs. Then we can cross multiply to get
$27 w - 27 = 3 {w}^{3} - 27 {w}^{2} + 24 w$

Get all terms to one side of the equation
$3 {w}^{3} - 27 {w}^{2} - 3 w + 27 = 0$

To make things easier, we divide the whole thing by 3
${w}^{3} - 9 {w}^{2} - w + 9 = 0$

We then factor the equation
$\left(w - 9\right) \left(w + 1\right) \left(w - 1\right) = 0$

We then solve for each factor
$w - 9 = 0$
$w = 9$

$w + 1 = 0$
$w = - 1$

$w - 1 = 0$
$w = 1$