Given: X = r + 2, Y = 2 r - 9, and Z = r2 + 17 r + 30. Simplify [X · Y - Z] : X.

Substituting the given formulas: (r+2) (2r-9) - (r^2+17r+30) / r+2

1. {multiply} (r+2) (2r-9) = 2r^2-5r-18

2. 2r^2-5r-18 - (r^2+17r+30) {distribute the negative sign} - (r^2+17r+30) becomes

-r^2-17r-30

3. {combine like terms} 2r^2-5r-18-r^2-17r-30 = r^2-22r-48

4. r^2-22r-48/r+2 (simplified)