Expert: Richard J. Raridon - 10/1/2009

Question
QUESTION: Hello. This is quite puzzling for me as i don't know the exact way to solve this.

Simplify:

a^2 - a - 12          a + 3
______________    ÷     __________

    9 - a          a + 4


Thanks for your help.

I'm very interested in knowing what rules apply here.

ANSWER: you can factor a^2-a-12 into (a-4)(a+3) so you have
(a-4)(a+3)(a+4)/[(9-a)(a+3)] = (a-4)(a+4)/(9-a)

---------- FOLLOW-UP ----------

QUESTION: Thanks.

I was more interested in the entire process.

Could you expand upon your answer?

Answer
OK, you have (a-4)(a+3)/(9-a) divided by (a+3)/(a+4)
You flip over to get the expression I gave you above and then cancel the (a+3)'s
What have you been learning?

In the past four years I have answered 3200 questions on this web site, doing it for fun.  My ratings range from 9.66 to 9.92.  If you had told me you were 13 years old, I probably would have given more explanation, but I don't have time to go into detail with every answer.