1/x + 1/y = ...

1) $\frac{1}{x} + \frac{1}{y} = \frac{y+x}{xy}$ 2) $\frac{1}{a} - \frac{1}{b} = \frac{b-a}{ab}$ 3) $\frac{x}{y^2} \cdot \frac{xy}{3} = \frac{x^2y}{3y^2} = \frac{x^2}{3y}$ 4) $\frac{x}{2y} + \frac{y}{x} = \frac{x^2+2y^2}{2xy}$ 5) $\frac{a+5}{3a} \cdot \frac{a^2}{a+5} = \frac{a}{3}$ 6) $\frac{25}{x} : \frac{10}{x^2} = \frac{25}{x} \cdot \frac{x^2}{10} = \frac{5x}{2}$ 7) $\frac{x}{x+3} + \frac{3}{x+3} = \frac{x+3}{x+3} = 1$ 9) $\frac{a}{b-1} \cdot \frac{b-1}{2} = \frac{a}{2}$ 10) $\frac{3x}{a-2} \cdot \frac{2-a}{9} = \frac{3x}{a-2} \cdot \frac{-(a-2)}{9} = -\frac{x}{3}$ 11) $\frac{a}{2} + \frac{a-5}{3} = \frac{3a + 2(a-5)}{6} = \frac{5a-10}{6}$ 12) $\frac{3}{x(x+5)} \cdot \frac{2(x+5)}{x} = \frac{6}{x^2}$ 13) $\frac{2}{a-2} + \frac{2}{a} = \frac{2a + 2(a-2)}{a(a-2)} = \frac{4a-4}{a(a-2)}$ 14) $\frac{6y+1}{2x} : \frac{1}{x} = \frac{6y+1}{2x} \cdot x = \frac{6y+1}{2}$ 15) $\frac{b+2}{b^2-9} - \frac{b}{9-b^2} = \frac{b+2}{b^2-9} + \frac{b}{b^2-9} = \frac{2b+2}{b^2-9}$