2. Упростите выражение 1) 2/x + (3x-2)/(x+1) ; 2) a/(a-3) - 3/(a+3) ; 3) x/(2y+1) - x/(3y-2)

1) $$ \frac{2}{x} + \frac{3x-2}{x+1} = \frac{2(x+1) + x(3x-2)}{x(x+1)} = \frac{2x + 2 + 3x^2 - 2x}{x(x+1)} = \frac{3x^2 + 2}{x(x+1)} $$.

2) $$ \frac{a}{a-3} - \frac{3}{a+3} = \frac{a(a+3) - 3(a-3)}{(a-3)(a+3)} = \frac{a^2 + 3a - 3a + 9}{a^2 - 9} = \frac{a^2 + 9}{a^2 - 9} $$.

3) $$ \frac{x}{2y+1} - \frac{x}{3y-2} = \frac{x(3y-2) - x(2y+1)}{(2y+1)(3y-2)} = \frac{3xy - 2x - 2xy - x}{(2y+1)(3y-2)} = \frac{xy - 3x}{(2y+1)(3y-2)} $$.

Ответ: 1) $$\frac{3x^2 + 2}{x(x+1)}$$; 2) $$\frac{a^2 + 9}{a^2 - 9}$$; 3) $$\frac{xy - 3x}{(2y+1)(3y-2)}$$