(5x+6)/(x^2-4) - (x+3)/(x-2) : (x^2+5x+6)/( x-2
)=
=(5x+6)/(x-2)(x+2) - (x+3)/(x-2) : (x+2)(x+3)/( x-2
)=
=(5x+6)/(x-2)(x+2) - (x+3)/(x-2) × ( x-2
)/(x+2)(x+3)=
=(5x+6)/(x-2)(x+2) - 1/(x+2)=
=(5x+6-x+2)/(x-2)(x+2)=
=(4x+8)/(x-2)(x+2)=
=4(x+2)/(x-2)(x+2)=
=4/(x-2)