Question

已知,y=(x^2+2x+1/x^2-1)÷(x+1/x^2-x)-x+1,是说明不论x为何值时,y的值不变

Answer 1

棉清：

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

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

=[(x+1)/(x-1)]×[x(x-1)/(x+1)]-x+1

=x-x+1

=1

∴不论x为何值时,y的值不变,都为1