5)а)(3x + y)/(2x - y) + (-2y - x)/(2x - y) = (3x + y + (-2y)- x)/(2x - y) = (4x - y)/(2x - y)
б)(6a - 3b)/(2a - b) - 1 = 3(2a - b)/(2a - b) - (2a - b)/(2a - b) = ((6a - 3b) - (2a - b))/
/(2a - b) = (6a - 3b - 2a + b)/(2a - b) = (4a - 2b)/(2a - b) = 2(2a - b)/(2a - b) = 2
6) а)(m² - 64n²)/(3m - 24n) = (m - 8n)(m + 8n)/3(m - 8n) = (m + 8m)/3
б)(x² - 6x + 9)/(x² - 9) = (x - 3)²/(x² - 9) = (x - 3)(x - 3)/(x - 3)(x + 3) = (x - 3)/(x + 3)
7) 2/(x - 4) - (x + 8)/(x² - 16) - 1/x = 2/(x - 4) - (x + 8)/(x - 4)(x + 4) - 1/x = x(x + 4) · 2/
/(x - 4)(x + 4)x - x(x + 8)/x(x - 4)(x + 4) - (x - 4)(x + 4)/x(x - 4)(x + 4) = (2x² + 8x)/
(x - 4)(x + 4)x - x(x + 8)/(x - 4)(x + 4)x - (x - 4)(x + 4)/(x - 4)(x + 4)x = (2x² + 8x) -
+ x(x + 8) - (x - 4)(x + 4)/(x - 4)(x + 4)x = (2x² + 8x - x² - 8x - (x² - 16))/(x - 4)(x + 4)x
= (2x² + 8x - x² - 8x - x² + 16)/(x - 4)(x + 4)x = 16/(x² - 16)x = 16/(x³ - 16)
8)x/(x + y) + 2xy/(x² - y²) - y/(x - y) = 1
x/(x + y) + 2xy/(x² - y²) - y/(x - y) = x(x - y)/(x + y)(x - y) + 2xy/(x - y)(x + y) - (x + y)y/
/(x - y)(x + y) = x(x - y) + 2xy - (x + y)y/(x + y)(x - y) = (x² - xy + 2xy - xy - y²)/(x + y)
(x - y) = (x² - y²)/(x² - y²) = 1
1 = 1