Simplify the following algebraic expressions: 1) (3x+6)/3 2) (7a2b + 14ab2)/(7ab) 3) (3p5 + 15p4 - 9p3)/(3p2)

$$\frac{3x}{3} + \frac{6}{3} = x + 2$$

The simplified expression is $\boxed{\mathbf{x+2}}$.

2) Simplify $\frac{7a^2b + 14ab^2}{7ab}$

$$\frac{7a^2b}{7ab} + \frac{14ab^2}{7ab} = (a^{2-1}b^{1-1}) + (2a^{1-1}b^{2-1})$$ $$= (a^1b^0) + (2a^0b^1)$$

Since $b^0 = 1$ and $a^0 = 1$:

$$= a + 2b$$

The simplified expression is $\boxed{\mathbf{a+2b}}$.

3) Simplify $\frac{3p^5 + 15p^4 - 9p^3}{3p^2}$

$$\frac{3p^5}{3p^2} + \frac{15p^4}{3p^2} - \frac{9p^3}{3p^2} = (p^{5-2}) + (5p^{4-2}) - (3p^{3-2})$$ $$= p^3 + 5p^2 - 3p$$

The simplified expression is $\boxed{\mathbf{p^3+5p^2-3p}}$.