Question

已知x^2-2=0,则式子(x-1)^2/x^2-1 + x^2/x+1的值为

Answer 1

原式=（x-1)^2/(x^2-1)+x^2(x-1)/(x^2-1)

=((x-1)^2+x^2(x-1))/(x^2-1)

=(x-1)(x-1+x^2)/(x^2-1) 因为x^2=2

=(x-1)(x-1+2)/(x^2-1)

=(x-1)(x+1)/(x^2-1)

=1