第1章 1.41

(1)

$\frac{7ab^2}{12x^2y} \times \frac{8bx}{21a^2y} \div \frac{b^2}{9ay^3} = \frac{2b^3}{9xy^2a} \times \frac{9ay^3}{b^2} = \frac{2by}{x}$

(2)

$\frac{(-xy)^2}{z} \times \frac{3z^2}{x^3y} \div \frac{6yz}{(-zy^2)^3} = \frac{3yz}{x} \times \frac{z^3y^6}{6yz} = -\frac{y^6z^3}{2x}$

(3)

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

(4)

$\frac{u^2+2u-3}{u^2-4} \times \frac{u^2+5u-14}{u^2+8u+15} = \frac{(u+3)(u-1)}{(u-2)(u+2)} \times \frac{(u+7)(u-2)}{(u+3)(u+5)} = \frac{(u-1)(u+7)}{(u+2)(u+5)} = \frac{u^2+6u-7}{u^2+7u+10}$

(5)

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

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

(6)

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