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.