a. 1/2x-y + 3y/y²-4x²-2/2x+y
= 1/2x-y + 3y/ (y-2x)(y+2x) + 2/2x+y
= 2x+y/(2x+y)(2x-y)+3y/(2x-y)(2x+y)-4x/(2x+y)(2x-y)
=2x+y+3y-4x-2y/(2x-y)(2x+y)
=-2
b. x²-9y²/x²y × 3xy/x²-3y²
=(x²-9y²) × 3xy/x²y × (x²-3y²)
= (x-3y)(x+3y)-3xy/x²y × (x-3y)(x+3y)
= -3/x
c. x+y/y-x ÷ x²-xy/2x²-2y²
= x+y/y-x × 2x²-2y/x²-xy
= x+y/x+y × 2(x²-y²)/x(x-y)
= x+y-2 × (x-y)(x+y)/(x+y) × x(x-y)
= y-2/x