42517 ÷ 9 = 4724 R1
Alright, let's work through the division of 42517 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 (1) of the dividend behind the 2 and repeat the process: 21 / 9

Step 4:
9 goes into 21 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 472
Subtract 18 from 21 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 5:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4724
Subtract 36 from 37 to get 1.

The final result is 4724 with a remainder of 1.