To simplify the expression (x+3)/(2x-4) * x^2-4/(3x+9), we first need to simplify each part individually.

Simplify (x+3)/(2x-4):

(x+3)/(2x-4) can be simplified by factoring out a common factor of 1 from the numerator and denominator:

(x+3)/(2x-4) = (x+3)/(2(x-2))

Simplify x^2-4:

x^2-4 can be factored as a difference of two squares: (x+2)(x-2)

Simplify 4/(3x+9):

4/(3x+9) can be simplified by factoring out a common factor of 4:

4/(3x+9) = 4/3(x+3)

Now, putting all the simplified parts together:

((x+3)/(2x-4)) (x^2-4/(3x+9)) = ((x+3)/(2(x-2))) ((x+2)(x-2))/(4/3(x+3))

Next, simplify by canceling out common factors:

((x+3)/(2(x-2))) ((x+2)(x-2))/(4/3(x+3)) = (x+2)/(2) (x+2) = (x+2)^2/2

Therefore, the simplified expression is (x+2)^2/2.