Express
3x+5(x+1)(x+2)\displaystyle \frac{3x+5}{(x+1)(x+2)}(x+1)(x+2)3x+5
in the form
Ax+1+Bx+2\displaystyle \frac{A}{x+1}+\frac{B}{x+2}x+1A+x+2B
where A A\,A and B B\,B are integers.