How would you subtract and simplify this?

Question

(x / x^2 + 5x + 6) - (2 / x^2 + 3x + 2)

Answer 1

the denominator of the first fraction has roots x=-2 and x=-3
so it can be written (x+3) (x+2)
the denominator of the second fraction has roots x=-2 and x=-1
so it can be written (x+1) (x+2)

and ((x/(x+3) (x+2))-2/((x+1) (x+2))
you use as common denominator (x+1)(x+2) (x+3)

(x*(x+1)-2(x+3))/(x+1)(x+2) (x+3)

result (x^2-x-6)/(x+1)(x+2) (x+3)

Roots of numerator -3 and +2

(x+3)(x-2)/(x+1)(x+2) (x+3)

Final result (x-2)/(x+1)(x+2)= (x-2)/(x^2+3x+2)