Question

化简,求值:x^2-x/x^2-2x+1-x/x+1,其中x=根号2

大家速度啦 0.0拜托

Answer 1

(x^2-x)/(x^2-2x+1)-x/(x+1)
=x(x-1)/(x-1)^2-x/(x+1)
=x/(x-1)-x/(x+1)
=x(x+1)/[(x-1)(x+1)]-x(x-1)/[(x-1)(x+1)]
=[x(x+1)-x(x-1)]/[(x-1)(x+1)]
=[x^2+x-x^2+x]/[(x-1)(x+1)]
=2x/[(x-1)(x+1)]
=2x/(x^2-1)
=2√2/[(√2)^2-1]
=2√2

Answer 2

原式=x(x-1)/(x-1)²-x/(x+1)
=x/(x-1)-x/(x+1)
=x(x+1)/(x-1)(x+1)-x(x-1)/(x+1)(x-1)
=(x²+x-x²+x)/(x²-1)
=2x/(x²-1)
当x=√ 2时
原式=2√2/(2-1)=2√2

Answer 3

x^2-x/x^2-2x+1-x/x+1中间是怎么断开的？请在详细点，以免弄错。