(x+1-1/1-x)÷(x-x²/x-1)
=[(x+1)+1/(x-1)]×[-(x-1)/x(x-1)]
=(x²-1+1)/(x-1)×(-1/x)
=-x/(x-1)

(x-4/x²-x-6+ x+2/x-3)÷x+1/x-3
=[(x-4)+(x+2)²]/(x+2)(x-3)×(x-3)/(x+1)
=(x²+5x)/(x+2)(x+1)