A) ((x - y)/2x)² · ((4x/(x - y)) + 4x/y) = (x - y)²/(2x)² · ((4x/(x - y)) + 4x/y) = (x - y)²/(2x)² ·
· (4x/(x - y)) + (x - y)²/(2x)² · 4x/y = (x - y)/y
1) (x - y)²/(2x)² · (4x/(x - y)) = (x - y)(x - y)/4x² · 4x/(x - y) = (x - y)(x - y)4x/4x²(x - y) =
= (x - y)/x
2) (x - y)²/(2x)² · 4x/y = (x - y)(x - y)/4x² · 4x/y = (x - y)(x - y)4x/4x²y = (x - y)(x - y)/xy
3) (x - y)/x + (x - y)(x - y)/xy = y(x - y)/xy + (x - y)(x - y)/xy = y(x - y) + (x - y)(x - y)/xy =
= (xy - y² + x² - 2xy + y²)/xy = (x² - xy)/xy = x(x - y)/xy = (x - y)/y
b) (x - (5x - 16)/(x - 3)) ÷ (3x - (3x/(x - 3))) = (x - 4)/3x
1) (x - (5x - 16)/(x - 3)) = x(x - 3)/(x - 3) - (5x - 16)/(x - 3) = (x(x - 3) - (5x - 16))/(x - 3) =
= (x² - 3x - 5x + 16)/(x - 3) = (x² - 8x + 16)/(x - 3) = (x - 4)(x - 4)/(x - 3)
2) (3x/1 - (3x/(x - 3))) = (3x(x - 3)/(x - 3) - (3x/(x - 3)) = (3x(x - 3) - 3x)/(x - 3) = (3x² -
- 9x-3x)/(x - 3) = (3x² - 12x)/(x - 3) = 3x(x - 4)/(x - 3)
3) (x - 4)(x - 4)/(x - 3) ÷ 3x(x - 4)/(x - 3) = (x - 4)(x - 4)/(x - 3) · (x - 3)/3x(x - 4) = (x - 4) · · (x - 4)(x - 3)/(x - 3) · 3x(x - 4) = (x - 4)/3x