简便计算以下各题：
(1) $17.2 \div \frac{12}{11} - 1.2 \times \frac{11}{12}$
(2) $\frac{5}{9} \div 4 + \frac{3}{4} \times \frac{5}{9}$
(3) $\frac{3}{8} \times \frac{8}{9} \div \frac{5}{6}$

1. 将除法转化为乘倒数，显现公因数

$17.2 \div \frac{12}{11} - 1.2 \times \frac{11}{12} = 17.2 \times \frac{11}{12} - 1.2 \times \frac{11}{12}$

2. 运用乘法分配律逆运算提取公因数并计算

$\begin{aligned} &= (17.2 - 1.2) \times \frac{11}{12} \\ &= 16 \times \frac{11}{12} \\ &= \frac{4 \times 11}{3} \\ &= \frac{44}{3} \quad (\text{或 } 14\frac{2}{3}) \end{aligned}$

1. 将除法转化为乘倒数，显现公因数

$\frac{5}{9} \div 4 + \frac{3}{4} \times \frac{5}{9} = \frac{5}{9} \times \frac{1}{4} + \frac{3}{4} \times \frac{5}{9}$

2. 提取公因数并结合加法凑整

$\begin{aligned} &= \frac{5}{9} \times \left(\frac{1}{4} + \frac{3}{4}\right) \\ &= \frac{5}{9} \times 1 \\ &= \frac{5}{9} \end{aligned}$

1. 将除法改写为乘倒数并统一分子分母进行约分

$\begin{aligned} \frac{3}{8} \times \frac{8}{9} \div \frac{5}{6} &= \frac{3}{8} \times \frac{8}{9} \times \frac{6}{5} \\ &= \frac{3 \times 8 \times 6}{8 \times 9 \times 5} \\ &= \frac{18}{45} \\ &= \frac{2}{5} \end{aligned}$