Question 663799
Note: I'm going to use 'x' in place of 'a'

Use polynomial long division to get 


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/10-9-20123-06-46PM.png">


So we can see that the quotient is {{{5x+2}}} and the remainder is {{{3}}}


This means {{{(10x^2+19x+9)/(2x+3) = 5x+2}}} Remainder {{{3}}}


Which can also be written as {{{(10x^2+19x+9)/(2x+3) = 5x+2+3/(2x+3)}}}