{[(x)/(x-1)]-[(x)/(x^2-1)]}÷[(x^2-x)/(x^2-2x+1)]

问题描述:

{[(x)/(x-1)]-[(x)/(x^2-1)]}÷[(x^2-x)/(x^2-2x+1)]

原式 = [x/(x – 1)– x/(x 2 –1)] / [x(x – 1)/(x – 1) 2 ] = [(x + 1)/(x 2 –1) – 1/(x 2 –1)] / [1/(x – 1)] = [x/(x 2 –1)]*(x – 1) = x/(x + 1) .