Expert: Ahmed Salami - 6/23/2004

Question
How doing you solve and simplify the following:

2x^2 - 11x + 12                   3x^2 - 16x + 16
----------------    divided by    ----------------
6x^2 + x - 12                        4x^2 - 9

This is the answer that I got:

4x^2 - 12x + 9
----------------         
9x^2 - 24x + 16


I am not sure if this answer can be simplified more.  Please tell me if I am on the right track.  

Answer
Hi Kayla,
let
A = (2x^2 - 11x + 12) / ( 6x^2 + x - 12)
 = (x - 4)(2x - 3) / (3x - 4)(2x + 3)  
B = (3x^2 - 16x + 16)( 4x^2 - 9)
 = (x - 4)(3x - 4) / (2x + 3)(2x - 3)
Therefore,
A/B = (x - 4)(2x - 3)(2x + 3)(2x - 3) /
(3x - 4)(2x + 3)(x - 4)(3x - 4)
      = (2x - 3)^2 / (3x - 4)^ 2
which cannot be simplified further.
this is the same as your answer, but in this form it is clearly seen that further simplification is not possible.
i hope you understand.
Regards.