9x^2-4/x^2+9x+20 divided by 3x^2+5x+2/x^2+5x+4 multiplied by x^2+3x-10/x^2+x-6?

Question

I need to know how to solve this problem; there are no examples in my math book yet it's on a test. Set up for failure? I think so!

Answer 1

9x^2 - 4 = (3x - 2) (3x + 2)

x^2 + 9 + 20 = (x + 5) (x + 4)

3x^2 + 5x + 2 = (3x +2) (x +1)

x^2 + 5x + 4 = (x +4) (x + 1)

x^2 + 3x - 10 = (x + 5) (x - 2)

x^2 + x - 6 = (x +3) (x - 2)

then substitute :          (3x - 2) (3x + 2)
                                       --------------------
                                        (x + 5) (x + 4)                         (x + 5) (x -2)
                              --------------------------------     .      -------------------
                                       (3x + 2) (x + 1)                       (x +3) (x -2)
                                      --------------------
                                        (x + 4) (x + 1)
then:

                           (3x - 2) (3x + 2)          (x + 4) (x + 1)           (x + 5) (x -2)
                          ----------------------       -------------------        ------------------
                             (x + 5) (x + 4)          (3x + 2) (x + 1)           (x +3) (x -2)

then cancel all the equation that is thesame at the numerator and demonitor

              (3x + 2) , (x + 5) , (x + 4) , (x + 1) and (x - 2)

                                               (3x - 2)
  then what is left is           ------------ 
                                                (x +3)