原式=x+1/(x-1)-(x²-3x+4)/(x²-1)
=x+(x+1)/(x+1)(x-1)-(x²-3x+4)/(x+1)(x-1)
=x+(x+1-x²+3x-4)/(x+1)(x-1)
=x-(x²-4x+3)/(x+1)(x-1)
=x-(x-1)(x-3)/(x+1)(x-1)
=x-(x-3)/(x+1)
=(x²+x-x+3)/(x+1)
=(x²+3)/(x+1)