`\frac{x}{x-3} - \frac{x^2+3x}{2x+3} * (\frac{x+3}{x^2-3x} - \frac{x}{x^2-9})`

`= \frac{x}{x-3}-\frac{x^{2}+3x}{2x+3} \cdot (\frac{x+3}{x+3} \cdot \frac{x+3}{(x-3)x}+\frac{x}{x} \cdot \frac{-x}{(x-3)(x+3)})`

`= \frac{x}{x-3}-\frac{x^{2}+3x}{2x+3} \cdot (\frac{(x+3)^{2}}{x(x-3)(x+3)}+\frac{x(-x)}{x(x-3)(x+3)})`

`= \frac{x}{x-3}-\frac{x^{2}+3x}{2x+3} \cdot (\frac{(x+3)^{2}+x(-x)}{x(x-3)(x+3)})`

`= \frac{x}{x-3}-\frac{x^{2}+3x}{2x+3} \cdot (\frac{6x+9}{x(x-3)(x+3)})`

`= frac{x}{x-3}-\frac{(x^{2}+3x)(6x+9)}{(2x+3)x(x-3)(x+3)}`

`= \frac{x}{x-3}-\frac{3}{x-3}`

`= \frac{x-3}{x-3}`

`= 1`