Express
x+5(x+2)(x+3)\displaystyle \frac{x + 5}{(x + 2)(x + 3)}(x+2)(x+3)x+5
in the form
Ax+2+Bx+3\displaystyle \frac{A}{x + 2} + \frac{B}{x + 3}x+2A+x+3B
where A A\,A and B B\,B are integers.