Question 722036
21a-14a^2           6a^2+11a+3
__________    .    ____________

9a^2+6a+1             4a^2-9


You mean THIS:
{{{((21a-14a^2)/(9a^2+6a+1))*((6a^2+11a+3)/(4a^2-9))}}}



Factor everything that you can.
{{{(7a(3-2a)/(3a+1)^2)*((2a+3)(3a+1)/((2a+3)(2a-3)))}}}

Begin eliminating any redundant factors of 1 that you can.  See the 3a+1?
{{{(7a(3-2a)/(3a+1))*((2a+3)/((2a+3)(2a-3)))}}}, what else?  2a+3?
{{{(7a(3-2a)/(3a+1))*(1/((2a-3)))}}}, and still more.


Note that {{{3-2a=-1*(2a-3)}}}.
{{{(7a(3-2a)/(3a+1))*(1/((2a-3)))}}}
={{{(7a(-1)(2a-3)/(3a+1))*(1/((2a-3)))}}}
={{{(7a(-1)/(3a+1))*(1/(1))}}}
When all simplified, result is {{{highlight((-7a/(3a+1)))}}}