Determining g(x)?

$\ h(x)\ =\ f(x)\cdot g(x)$

                                          Divide both sides of the equation by  f(x)

$\dfrac{h(x)}{f(x)}\ =\ g(x)$

                                          Substitute  6x + 15  in for  h(x)  and substitute  2x + 5  in for  f(x)

$\frac{6x+15}{2x+5}\ =\ g(x)$

                                          That is the same as....

$g(x)\ =\ \frac{6x+15}{2x+5}$

                                          We can factor  3  out of  6x + 15  because  3(2x + 5)  =  6x + 15

$g(x)\ =\ \frac{3(2x+5)}{2x+5}$

                                          Cancel the common factor of  (2x + 5)  in the numerator and denominator.

$g(x)\ =\ 3$          and note that   2x + 5  ≠  0   so   x  ≠  -5/2

So we can say     g(x)  =  3     for all possible values of  x  except  x = -5/2