Question 102007
{{{ ((3x^2 + 13x + 4) / (16 - x^2)) / ((3x^2 -5x -12) / (3x - 12)) }}}
{{{ ((3x^2 + 13x + 4) / (16 - x^2)) * ((3x - 12) / (3x^2 -5x -12)) }}}
{{{ highlight((3x^2 + 13x + 4) * (3x - 12)) / ((16 - x^2) * (3x^2 -5x -12)) }}}

First, factorize the highlighted part.

{{{ (3x^2 + 13x + 4) * (3x - 12) }}}
{{{ (3x + 1)*(x + 4) * 3*(x - 4) }}}

Therefore,

{{{ ((3x + 1)*(x + 4) * 3*(x - 4)) / highlight((16 - x^2) * (3x^2 -5x -12)) }}}

Again, with the highlighted part

{{{ (16 - x^2) * (3x^2 -5x -12) }}}
{{{ (4 - x)*(4 + x) * (3x + 4)*(x - 3) }}}
or
{{{ -1 * (x - 4)*(x + 4) * (3x + 4)*(x - 4) }}}

So the original problem becomes

{{{ ((3x + 1)*(x + 4) * 3*(x - 4)) / (-1 * (x - 4)*(x + 4) * (3x + 4)*(x - 4)) }}}

Some of the factors cancel each other, therefore:

{{{ ((3x + 1)*cross((x + 4)) * 3*cross((x - 4))) / (-1 * cross((x - 4))*cross((x + 4)) * (3x + 4)*(x - 4)) }}}

It can't be simplified any further, so the answer would be

{{{ - 3 * (3x + 1) / (3x + 4) / (x - 3) }}}

Hope that'll help.