Synthetic division help

(2x^3-x+5)/(2x-3) is the problem, and it has to be done with synthetic division. So if you could use that to teach me how to do it that would be great!

2x - 3 = 0 ----> x = 3/2

First, divide by (x − 3/2) using synthetic division:
http://www.purplemath.com/modules/synthd…

3/2 | 2 .. 0 ..... −1 ....... 5
..... | ..... 3 .... 9/2 .... 21/4
----------------------------------
....... 2 .. 3 .... 7/2 ... 41/4

2x³ + 0x − x + 5 = (x − 3/2) (2x² + 3x + 7/2) + 41/4
2x³ − x + 5 = 1/2 * 2(x − 3/2) (2x² + 3x + 7/2) + 41/4
2x³ − x + 5 = (2x − 3) * 1/2 (2x² + 3x + 7/2) + 41/4
2x³ − x + 5 = (2x − 3) (x² + 3/2 x + 7/4) + 41/4

(2x³ − x + 5) / (2x − 3) = (x² + 3/2 x + 7/4) + (41/4) / (2x − 3)

..............x^2 + 3x/2 + 7/4 + R(41/4)
............---------------------------…
2x - 3 | 2x^3 + 0x^2 - x + 5
.............2x^3 - 3x^2
.............------------------
.............0x^3 + 3x^2 - x
......................+ 3x^2 - 9x/2
............................-----------…
............................0x^2 +7x/2 + 5
.....................................+7… - 21/4
......................................-…
.......................................…


So we get:

x^2 + (3/2) * x + (7/4) + (41/4) / (2x - 3)