Question

已知x是一元二次方程x²+3x-1=0的实数根,那么代数式x-3/3x²-6x ÷(x+2- 5/x-2)的值为？

Answer 1

x²+3x-1=0
x²+3x=1

原式=[(x-3)/3x(x-2)]÷[(x²-4-5_)/(x-2)]
=[(x-3)/3x(x-2)]×[(x-2)/(x-3)(x+3)]
=1/3x(x+3)
=1/[3(x²+3x)]
=1/3