Question

问（x-1/x-2）-（x-2/x-3）-（x-3/x-4）+（x-4/x-5）的值拜托各位大神

Answer 1

原式=(x-2+1)/(X-2) - (X-3+1)/(X-3) - (X-4+1)/(X-4)+(X-5+1)/(X-5) =1+ 1/(X-2) -1 - 1/(X-3) -1 - 1/(X-4) +1 + 1/(X-5) =1/(X-2) + 1/(X-5) - 1/(X-3) - 1/(X-4) =(X-5+X-2)/(X-2)(X-5) - (X-4+X-3)/(X-3)(X-4) =(2X-7)/(X^2-7X+10) - (2X-7)/(X^2-7X+12) =(2X-7)[1/(X^2-7X+10) - 1/(X^2-7X+10+2) 换元；令y=X^2-7X+10,得 原式=（2x-7)[ 1/y - 1/（y+2)]=(2X-7)[2/(y^2+2y)] =(4x-14)/(x-2)(x-3)(x-4)(x-5)