Question

分式计算：（1+1/x）÷[（x+4）/（1-x)-(x²-x-2)/(x²-1)(过程）

Answer 1

(x²-x-2)/(x²-1) = [(x-2)(x+1)]/[(x-1)(x+1)] = (x-2)/(x-1)

故（x+4）/（1-x)-(x²-x-2)/(x²-1)=(2x+2)/(1-x)

（1+1/x）÷(2x+2)/(1-x) =[(1-x)(1+x)]/[x(2x+2)]=(1-x)/2x= (1/x-1)*1/2