Question

x+1分之x+2-（x+2分之x+3）+x-4分之x-5-（x-3分之x-4）求化简此分式

请化简该分式，谢谢！

Answer 1

(x+2)/(x+1)=(x+1+1)/(x+1)=1+1/(x+1)
其他一样
所以原式=1/(x+1)-1/(x+2)-1/(x-5)+1/(x-4)
=(x+2-x-1)/(x+1)(x+2)+(x-5-x+4)/(x-4)(x-5)
=1/(x²+3x+2)-1/(x²-9x+20)
=(-12x+18)/(x^4-6x³-5x²+42x+40)