原式=(x+2)/x(x+1)+(2x+1)/(x+1)(x+2)-(x-3)/x(x+2)
=[(x+2)^2+x(2x+1)-(x+1)(x-3)]/x(x+1)(x+2)
=(x^2+4x+4+2x^2+x-x^2+2x+3)/x(x+1)(x+2)
=(2x^2+7x+7)/(x^3+3x^2+2x)
原式=(x+2)/x(x+1)+(2x+1)/(x+1)(x+2)-(x-3)/x(x+2)
=[(x+2)^2+x(2x+1)-(x+1)(x-3)]/x(x+1)(x+2)
=(x^2+4x+4+2x^2+x-x^2+2x+3)/x(x+1)(x+2)
=(2x^2+7x+7)/(x^3+3x^2+2x)