Question

分式化简：[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)]/(x-4)/(x^3-2x^2)

Answer 1

[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)]/(x-4)/(x^3-2x^2)

=(x+2)x^2(x-2)/[x(x-2)(x-4)]-(x-1)x^2(x-2)/[(x-2)^2(x-4)]

=(x+2)x/(x-4)-(x-1)x^2/[(x-2)(x-4)]

=(x^3-4x-x^3+x^2)/[(x-2)(x-4)]

=x(x-4)/[(x-2)(x-4)]

=x/(x-2)