x^2-3x+2分之3x-7 + x^2-x-2分之2x-1 - x^2-1分之5x 的分式约分谢谢

题目

x^2-3x+2分之3x-7 + x^2-x-2分之2x-1 - x^2-1分之5x 的分式约分谢谢

答案

原式=(3X-7)/(x^2-3x+2)+(2x-1)/(x^2-x-2)-5x/(x^2-1)
=(3x-7)/[(x-2)(x-1)]+(2x-1)/[(x-2)(x+1)]-5x/[(x-1)(X+1)]
=[(3x-7)(x+1)]/[(x-2)(x-1)(x+1)]+[(2x-1)(x-1)]/[(x-2)(x-1)(x+1)]-5x(x-2)/[(x-2)(x-1)(x+1)]
=[3x^2-4x-7+2x^2-3x+1-5x^2+10x]/[(x-2)(x-1)(x+1)]
=(3x-6)/[(x-2)(x-1)(x+1)]
=3/[(x-1)(x+1)]
=3/(x^2-1)