第1章 1.23

(1)

$\frac{3a^2b}{a^3b} \times \frac{ab^2}{6a^2b} = \frac{b}{2a^2}$

(2)

$\frac{5a^2b}{6xy^2} \div \frac{3ab^2}{4x^2y} = \frac{5a^2b}{6xy^2} \times \frac{4x^2y}{3ab^2} = \frac{10ax}{9by}$

(3)

$\frac{2x^2+4x}{x^2-1} \times \frac{x-1}{x+2} = \frac{2x(x+2)}{(x-1)(x+1)} \times \frac{x-1}{x+2} = \frac{2x}{x+1}$

(4)

$\frac{a^2-b^2}{(a-b)^2} \div \frac{a+b}{a-b} = \frac{(a-b)(a+b)}{(a-b)^2} \times \frac{a-b}{a+b} = 1$

(5)

$\frac{t-3}{t+1} \times \frac{(t^2+5t+4)}{t^2-9} = \frac{t-3}{t+1} \times \frac{(t+1)(t+4)}{(t-3)(t+3)} = \frac{t+4}{t+3}$

(6)

$\frac{4a^2-1}{6a-8-a^2} \div \frac{2a^2+5a+2}{a^2-8-2a} = \frac{(2a-1)(2a+1)}{-(a-4)(a-2)} \times \frac{(a-4)(a+2)}{(2a+1)(a+2)} = -\frac{2a-1}{a-2}$

(7)

$\frac{a^2-4b^2}{3a^2+2ab} \times \frac{3a^2-ab-2b^2}{a^2-3ab+2b^2} = \frac{(a-2b)(a+2b)}{a(3a+2b)} \times \frac{(3a+2b)(a-b)}{(a-2b)(a-b)} = \frac{a+2b}{a}$