分式的加减 难题巧解题x+2 x+3 x-4 x-5—— - —— - —— - ——x+1 x+2 x-3 x-4

分式的加减 难题巧解题
x+2 x+3 x-4 x-5
—— - —— - —— - ——
x+1 x+2 x-3 x-4

(x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)-(x-5)/(x-4)
=[1+1/(x+1)]-[1+1/(x+2)]-[1-1/(x-3)]-[1-1/(x-4)]
=1+1/(x+1)-1-1/(x+2)-1+1/(x-3)-1+1/(x-4)
=1/(x+1)-1/(x+2)+1/(x-3)+1/(x-4)-2
=1/[(x+1)(x+2)]-1/[(x-3)(x-4)]-2