一个数学分式化简题

题目

一个数学分式化简题
2/x-1-2/x+1-1/x-2+1/x+2
3/2x+6-1/6-2x+3/9-x^2

答案

2/(x-1)-2/(x+1)-1/(x-2)+1/(x+2)
=2*(1/(x-1)-1/(x+1))-(1/(x-2)-1/(x+2))
=2*(x+1-x+1)/(x^2-1)-(x+2-x+2)/(x^2-4)
=4/(x^2-1)-4/(x^2-4)
=4*(1/(x^2-1)-1/(x^2-4))
=4*(x^2-4-x^2+1)/((x^2-1)*(x^2-4))
=4*(-3)/((x^2-1)*(x^2-4))
=-12/((x^2-1)*(x^2-4))
=-12/(x^4-5x^2+4)
3/(2x+6)-1/(6-2x)+3/(9-x^2)
=3/(2x+6)+1/(2x-6)+3/(9-x^2)
=(3*(2x-6)+2x+6)/(4x^2-36)+3/(9-x^2)
=(6x-18+2x+6)/(4x^2-36)+3/(9-x^2)
=(8x-12)/(4x^2-36)+3/(9-x^2)
=4*(2x-3)/(4*(x^2-9))-3/(x^2-9)
=(2x-3)/(x^2-9)-3/(x^2-9)
=(2x-3-3)/(x^2-9)
=(2x-6)/(x^2-9)
=(2*(x-3))/((x+3)*(x-3))
=2/(x+3)