What is the simplified form of (x+9)/8 minus (x+3)/(x+2)?

The simplified form of (x+9)/8 - (x+3)/(x+2) is:

x^2+3x-6 over 8 (x+2)

Work:

1. (x+9)(x+2) - (x+3) x 8 over 8 (x+2)

2. (x+9)(x+2) - 8(x+3) over 8(x+2)

3. x^2 + 2x + 9x + 18 - 8x -24 over 8(x+2)

4. x^2 + (2x + 9x - 8x) + (18 - 24) over 8(x+2)

= x^2+3x-6 over 8 (x+2)