To simplify the expression, let's first find a common denominator for the two fractions.

Let's first simplify the second fraction ((x^2 + 3x)/(4xy - 3 - 2y + 6x)):

(x^2 + 3x)/(4xy - 3 - 2y + 6x)

Factor out x from the numerator of the fraction:

x(x + 3)/(4xy - 3 - 2y + 6x)

Now, let's combine the two fractions by finding the common denominator. To do this, we need to multiply the first fraction by (4xy - 3 - 2y + 6x)/(4xy - 3 - 2y + 6x):

[(3x/(2y + 3)) * (4xy - 3 - 2y + 6x)/(4xy - 3 - 2y + 6x)] + [x(x + 3)/(4xy - 3 - 2y + 6x)]

Now, combine the two fractions by adding the numerators:

[(3x(4xy - 3 - 2y + 6x) + x(x + 3))/(4xy - 3 - 2y + 6x)] / (2y+3)

Expand and simplify:

(12xy - 9 - 6y + 18x + x^2 + 3x)/ (4xy - 3 - 2y + 6x)

Combine like terms:

(x^2 + 15x + 12xy - 6y - 9)/ (4xy - 3 - 2y + 6x)

Therefore, the simplified expression is:

(x^2 + 15x + 12xy - 6y - 9)/ (4xy - 3 - 2y + 6x)