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

Question

1487 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-28T14:12:48

#w=-1,1,9#

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

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

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

We then factor the equation
#(w-9)(w+1)(w-1)=0#

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

#w+1=0#
#w=-1#

#w-1=0#
#w=1#