Hi Saseflower,
It is WONDERFUL to see you!!
(x2 + 9x +14) • 9/3x + 21 (9 over 3x + 21, the whole thing)
I think the meaning of your question is clear but this is ideally how it could hve been presented.
(x^2+9x+14) * 9/(3x+21)
\((x^2+9x+14) * \frac{9}{3x+21}\\ =(x+2)(x+7) * \frac{9}{3(x+7)}\\ \mbox{ (x+7) cancels out because one is on the top and one is on the bottom.}\\ =(x+2) * \frac{9}{3}\\ =(x+2) * \frac{\not{9}^3}{\not{3}^1}\\ =(x+2) * 3\\ =3(x+2)\\ =3x+6 \)
I have not explained the initial factoring that I did in the first line. It is probably the hardest bit to understand.
Do you need me to explain more?? Which bits give you trouble.