235. Упростите выражение: a) 5 y-3 + 1/y+3 - 4y-18/y^2-9; б) 2a/2a +3 + 5/3-2a - 4a^2 +9/4a^2-9; В) 4m/4m^2-1 + 2m+1/6m-3 - 2m-1/4m+2;

Рассмотрим каждый пункт отдельно. a) $$\frac{5}{y-3} + \frac{1}{y+3} - \frac{4y-18}{y^2-9} = \frac{5(y+3) + (y-3) - (4y-18)}{(y-3)(y+3)} = \frac{5y + 15 + y - 3 - 4y + 18}{y^2 - 9} = \frac{2y + 30}{y^2 - 9} = \frac{2(y+15)}{y^2-9}$$ Ответ: $$\frac{2(y+15)}{y^2-9}$$. б) $$\frac{2a}{2a + 3} + \frac{5}{3-2a} - \frac{4a^2 + 9}{4a^2-9} = \frac{2a}{2a + 3} - \frac{5}{2a-3} - \frac{4a^2 + 9}{(2a-3)(2a+3)} = \frac{2a(2a-3) - 5(2a+3) - (4a^2 + 9)}{(2a-3)(2a+3)} = \frac{4a^2 - 6a - 10a - 15 - 4a^2 - 9}{4a^2 - 9} = \frac{-16a - 24}{4a^2 - 9} = \frac{-8(2a + 3)}{(2a-3)(2a+3)} = \frac{-8}{2a-3} = \frac{8}{3-2a}$$ Ответ: $$\frac{8}{3-2a}$$. в) $$\frac{4m}{4m^2-1} + \frac{2m+1}{6m-3} - \frac{2m-1}{4m+2} = \frac{4m}{(2m-1)(2m+1)} + \frac{2m+1}{3(2m-1)} - \frac{2m-1}{2(2m+1)} = \frac{4m \cdot 6 + (2m+1) \cdot 2(2m+1) - (2m-1) \cdot 3(2m-1)}{6(2m-1)(2m+1)} = \frac{24m + 2(4m^2 + 4m + 1) - 3(4m^2 - 4m + 1)}{6(4m^2-1)} = \frac{24m + 8m^2 + 8m + 2 - 12m^2 + 12m - 3}{6(4m^2-1)} = \frac{-4m^2 + 44m - 1}{6(4m^2-1)}$$ Ответ: $$\frac{-4m^2 + 44m - 1}{6(4m^2-1)}$$.