(6x³-8x²y+2xy²)÷(18x³-2xy²)

= 2x(3x^2 - 4xy + y^2) ÷ (2x(9x^2 - y^2) )
= (3x^2 - 4xy + y^2) ÷ ( (3x+y)(3x-y) ) , x ≠ 0

= (3x-y)(x-y) ÷ ( (3x+y)(3x-y) )

= (x-y) ÷ (3x+y) , x ≠ 0, y ≠ ±3x