SOLUTION: Help!! They're killing me. If only they would explain it in more Laymens terms; but they don't. I have been unable to figure out simplifying these type problems, same with multiply

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Question 102007This question is from textbook Intermediate Algebra
: Help!! They're killing me. If only they would explain it in more Laymens terms; but they don't. I have been unable to figure out simplifying these type problems, same with multiplying and simplifying, can some one show me the steps to solving when you divide and simplify, PLEASE?
Divide and Simplify:
3x^2 + 13x + 4
--------------
16 - x^2
Divided by:
3x^2 -5x -12
------------
3x - 12
Thank You eversomuch!! This question is from textbook Intermediate Algebra

Answer by mathemanic(13) About Me  (Show Source):
You can put this solution on YOUR website!



First, factorize the highlighted part.
+%283x%5E2+%2B+13x+%2B+4%29+%2A+%283x+-+12%29+
+%283x+%2B+1%29%2A%28x+%2B+4%29+%2A+3%2A%28x+-+4%29+
Therefore,

Again, with the highlighted part
+%2816+-+x%5E2%29+%2A+%283x%5E2+-5x+-12%29+
+%284+-+x%29%2A%284+%2B+x%29+%2A+%283x+%2B+4%29%2A%28x+-+3%29+
or
+-1+%2A+%28x+-+4%29%2A%28x+%2B+4%29+%2A+%283x+%2B+4%29%2A%28x+-+4%29+
So the original problem becomes

Some of the factors cancel each other, therefore:

It can't be simplified any further, so the answer would be
+-+3+%2A+%283x+%2B+1%29+%2F+%283x+%2B+4%29+%2F+%28x+-+3%29+
Hope that'll help.