42559 ÷ 9 = 4728 R7
Alright, let's work through the division of 42559 by 9 step by step.

Step 1:
9 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 9

Step 2:
9 goes into 42 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 36 from 42 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 9

Step 3:
9 goes into 65 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 47
Subtract 63 from 65 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 9

Step 4:
9 goes into 25 2 times with a remainder of 7.
Write down 2 as next digit of of the result. 
Result so far: 472
Subtract 18 from 25 to get 7.
Bring next digit (9) of the dividend behind the 7 and repeat the process: 79 / 9

Step 5:
9 goes into 79 8 times with a remainder of 7.
Write down 8 as next digit of of the result. 
Result so far: 4728
Subtract 72 from 79 to get 7.

The final result is 4728 with a remainder of 7.