To divide the expression (8x + 17) by (2x - 1), we can use long division.

4x + 9
_______________
2x - 1 | 8x + 17

First, divide 8x by 2x, which gives us 4x. Write this above the line.

4x + 9
_______________
2x - 1 | 8x + 17
- (8x - 4x)

Next, multiply (2x - 1) by 4x, which gives us 8x^2 - 4x. Write this below the line.

4x + 9
_______________
2x - 1 | 8x + 17
- (8x - 4x)
___________
8x^2 - 4x

Subtract (8x^2 - 4x) from (8x + 17), which gives us 0x^2 + 0x + 17. Write this below the line.

4x + 9
_______________
2x - 1 | 8x + 17
- (8x - 4x)
___________
8x^2 - 4x
- (8x^2 - 4x)
___________
0x^2 + 0x + 17

Since the degree of 0x^2 + 0x + 17 is less than the degree of 2x - 1, we cannot continue dividing. Therefore, the final result is:

(8x + 17) ÷ (2x - 1) = 4x + 9