2) а) 2/(x^2-y^2) + 3/(x+y);

Для сложения или вычитания дробей нужно привести их к общему знаменателю. 2) а) $\frac{2}{x^2-y^2} + \frac{3}{x+y} = \frac{2}{(x-y)(x+y)} + \frac{3(x-y)}{(x+y)(x-y)} = \frac{2+3x-3y}{(x-y)(x+y)}$ б) $\frac{a}{a-b} - \frac{a^2}{a^2-b^2} = \frac{a(a+b)}{(a-b)(a+b)} - \frac{a^2}{(a-b)(a+b)} = \frac{a^2+ab-a^2}{(a-b)(a+b)} = \frac{ab}{a^2-b^2}$ в) $\frac{5}{6m+6} - \frac{3}{2m+2} = \frac{5}{6(m+1)} - \frac{3}{2(m+1)} = \frac{5}{6(m+1)} - \frac{9}{6(m+1)} = \frac{-4}{6(m+1)} = \frac{-2}{3(m+1)}$ г) $\frac{6}{5x-10} + \frac{7}{3x-6} = \frac{6}{5(x-2)} + \frac{7}{3(x-2)} = \frac{18}{15(x-2)} + \frac{35}{15(x-2)} = \frac{53}{15(x-2)}$ д) $\frac{4b}{a^2+ab} - \frac{4}{a} = \frac{4b}{a(a+b)} - \frac{4(a+b)}{a(a+b)} = \frac{4b-4a-4b}{a(a+b)} = \frac{-4a}{a(a+b)} = \frac{-4}{a+b}$ е) $\frac{x}{3} - \frac{x^2}{3x+3y} = \frac{x}{3} - \frac{x^2}{3(x+y)} = \frac{x(x+y)-x^2}{3(x+y)} = \frac{x^2+xy-x^2}{3(x+y)} = \frac{xy}{3(x+y)}$ 3) а) $x + \frac{2}{x+4} = \frac{x(x+4)+2}{x+4} = \frac{x^2+4x+2}{x+4}$ б) $3 - \frac{a-2c}{a+c} = \frac{3(a+c)-(a-2c)}{a+c} = \frac{3a+3c-a+2c}{a+c} = \frac{2a+5c}{a+c}$ в) $b - 3 - \frac{1}{b+3} = \frac{(b-3)(b+3)-1}{b+3} = \frac{b^2-9-1}{b+3} = \frac{b^2-10}{b+3}$ г) $\frac{1}{a-2} + a - 1 = \frac{1 + (a-1)(a-2)}{a-2} = \frac{1 + a^2-2a-a+2}{a-2} = \frac{a^2-3a+3}{a-2}$ д) $2 + \frac{x}{y} + \frac{y}{x} = \frac{2xy + x^2 + y^2}{xy} = \frac{(x+y)^2}{xy}$ е) $\frac{a}{b} + \frac{b}{a} - 2 = \frac{a^2 + b^2 - 2ab}{ab} = \frac{(a-b)^2}{ab}$