a) (4xy -1 - 2xy +1)/5x^2y = 2xy/5x^2y= 2/5x
b) (x+8)/(x^2-16) - 2/(x^2 + 4x) = (x+8)/(x-4)(x+4) - 2/x(x+4) = x(x+8)/x(x-4)(x+4) - 2(x-4)/x(x+4)(x-4)
= (x^2 + 8x - 2x + 8)/x(x-4)(x+4)
= (x^2 + 4x + 2x + 8)/x(x-4)(x+4) 
= [[x(x+4) + 2(x+4)]]/x(x-4)(x+4)
= (x+2)(x+4)/x(x-4)(x+4)
= (x+2)/x(x-4)
c) (5xy -2)/xy^2 - (4xy -2)/xy^2
= (5xy- 2 - 4xy + 2)/xy^2
= xy/xy^2
= 1/y
d) (x+3)/(x^2-1) - 1/(x^2 + x)
= (x+3)/(x-1)(x+1) - 1/x(x+1)
= x(x+3)/x(x-1)(x+1) - (x-1)/x(x-1)(x+1)
= (x^2 + 3x - x + 1)/x(x-1)(x+1)
= (x^2 + 2x +1)/x(x-1)(x+1)
= (x+1)^2/x(x-1)(x+1)
= (x+1)/x(x-1)
e) (x+1)/(x-5) + (1-x)/(x+5)
= (x+1)(x+5)/(x-5)(x+5) + (1-x)(x-5)/(x-5)(x+5)
= (x^2 + 6x + 5 + x - x^2 - 5 + 5x)/(x-5)(x+5)
= 12x/(x+5)(x-5)
f) 4x/5 . 10/x^2
= 40x/5x^2
= 8/x
g) x/(x+3) . (x^2-9)/x^3
= x(x-3)(x+3)/x^3(x+3)
= (x-3)/x^2
h) 4y^2/10x^3 . -5x^2/8y^3
= -20x^2y^2/80x^3y^3
= -1/4xy
i) [[1/x - 1/(x+1)]] . (x^2 -1)/x
= [[(x+1)/x(x+1) - x/x(x+1)]] . (x-1)(x+1)/x
= (x+1 -x)/x(x+1) . (x-1)(x+1)/x
= 1/x(x+1) . (x-1)(x+1)/x
= (x-1)(x+1)/x^2(x+1)
= (x-1)/x^2