Question 1027738
me neither.


i graphed the factors and got the following graph.


the factors are (3x + 4 - sqrt(19)) * (3x + 4 + sqrt(19))


when you multiply those factors out, you get 9x^2 + 24x - 3.


i took that and then did the following:


start with 9x^2 + 24x - 3


subtract 24x from both sides to get:


9x^2 - 3 = -24x


factor the left side of the equation to get:


3 * (3x^2 - 1) = -24x


divide both sides of the equation to get:


3x^2 - 1 = -8x


divide both sides of the equation by 8x to get:


(3x^2 - 1) / 8x = -1


divide both sides of the equation by (3x^2 - 1) to get:


1 / 8x = -1 / (3x^2 - 1)


i then added -1 / (3x^2 - 1) to both sides of this equation to get:


1 / 8x + 1 / (3x^2 - 1) = 0


the roots of this equation are the same roots as the equation of 9x^2 + 24x - 3 = 0.


i graphed 3 equations to show you that the roots are the same for all 3.


the first 2 equations i graphed are:


y = (3x + 4 - sqrt(19)) * (3x + 4 + sqrt(19))


y = 9x^2 + 24x - 3.


these 2 equations are equivalent and show up as the same line on the graph.


the roots are x = -2.786 and x = .12


that graph is shown below:


<img src = "http://theo.x10hosting.com/2016/040206.jpg" alt="$$$" </>


the other equation i graphed is:


y = 1 / 8x + 1 / (3x^2 - 1)


that graph is shown below:


<img src = "http://theo.x10hosting.com/2016/040205.jpg" alt="$$$" </>


while this graph looks very different, the roots are the same.


the closest i could get to what you were showing with the roots you showed is:


start with:


9x^2 + 24x - 3 = 0


subtract 24x from both sides of the equation to get:


9x^2 - 3 = -24x


factor out the 3 on the left hand side to get:


3 * (3x^2 - 1) = -24x


divide both sides of the equation by 3 to get:


3x^2 - 1 = -8x


divide both sides of the equation by x and divide both sides of the equation by (3x^2 - 1) to get:


1/x = -8 / (3x^2 - 1)


that's the closest i could get to what you were showing.


it's not it.


what you are showing does not result in the roots you are showing.


i took the equation of 1/x = -8 / (3x^2 - 1) and added the right side of the equation to to both sides of the equation to get:


1/x + 8/(3x^2-1) = 0


the roots of that equation are the same, even though that equation looks different also.


the graph of y = 1/x + 8/(3x^2-1) is shown below.


<img src = "http://theo.x10hosting.com/2016/040207.jpg" alt=$$$" </>