(20:2 2/15+25 5/7:1 1/35):(21 7/9:4 2/3-1)

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To solve this expression, we can start by converting all the mixed numbers to improper fractions:

(207 + 2)/(157 + 25) : (219 + 7)/(93 + 4)

Now, we simplify the fractions:

(140 + 2)/(105 + 25) : (189 + 7)/(27 + 4)

142/130 : 196/31

Next, we simplify the fractions by finding a common denominator:

142/130 : 196/3
14231 / 13031 : 196130 / 3113
4402/4030 : 25480/4030

Now, we can divide the two fractions:

4402/4030 ÷ 25480/403
4402/4030 * 4030/2548
4402/25480

Therefore, the final answer is 4402/25480 or simplified, 221/1274.