Question

已知x²+3x-1=0,求(x-3)/(3x²-6x)÷（x+2-5/(x+2)）的值

Answer 1

x²+3x-1=0

x²+3x=1

(x-3)/3x²-6x）/[(x+2-5/(x-2)]

={(x-3)/[3x(x-2)]}/{[(x+2)(x-2)-5]/(x-2)]}

={(x-3)/[3x(x-2)]}/[(x²-9)/(x-2)]

={(x-3)/[3x(x-2)]}/{[(x+3)(x-3)]/(x-2)]}

=1/[3x(x+3)]

=1/[3(x²+3x)]

=1/3