第1章 1.21

(1)

$\frac{1}{2x} + \frac{1}{6x^2} = \frac{3x+1}{6x^2}$

(2)

$\frac{2c}{a^2b} - \frac{b}{a^2c} = \frac{2c^2 - b^2}{a^2bc}$

(3)

$\frac{3}{x+2} - \frac{2}{x+3} = \frac{3(x+3) - 2(x+2)}{(x+2)(x+3)} = \frac{x+5}{(x+2)(x+3)}$

(4)

$\frac{x}{x^2+x-6} + \frac{x+3}{x^2-3x+2} = \frac{x}{(x+3)(x-2)} + \frac{x+3}{(x-2)(x-1)} = \frac{x(x-1)+(x+3)^2}{(x+3)(x-2)(x-1)} = \frac{2x^2+5x+9}{(x+3)(x-2)(x-1)}$

(5)

$\frac{a+b}{a-b} - \frac{a-b}{a+b} = \frac{(a+b)^2 - (a-b)^2}{(a-b)(a+b)} = \frac{4ab}{a^2-b^2}$

(6)

$\frac{2xy}{x^2-y^2} + \frac{2y}{x-y} = \frac{2xy + 2y(x+y)}{x^2-y^2} = \frac{4xy+2y^2}{x^2-y^2}$