Here are the solutions to the mathematics problems: SUBJECT: MATHEMATICS a) Simplify (7x - 4) - (4x - 12) b) Solve the equation (x)/(3) + (x)/(2) = (5)/(2) a) Simplify ((x-3)(x+1))/(x)

$$
(7x - 4) - (4x - 12) = 7x - 4 - 4x + 12
$$

$$
(7x - 4x) + (-4 + 12)
$$

$$
3x + 8
$$
The simplified expression is:
$$
\boxed{3x + 8}
$$

**b)** Solve the equation $\frac{x}{3} + \frac{x}{2} = \frac{5}{2}$

$$
6 \left(\frac{x}{3}\right) + 6 \left(\frac{x}{2}\right) = 6 \left(\frac{5}{2}\right)
$$

$$
2x + 3x = 15
$$

$$
5x = 15
$$

$$
x = \frac{15}{5}
$$
$$
x = 3
$$
The solution for $x$ is:
$$
\boxed{x = 3}
$$

$$
(x-3)(x+1) = x(x) + x(1) - 3(x) - 3(1)
$$
$$
= x^2 + x - 3x - 3
$$
$$
= x^2 - 2x - 3
$$

$$
\frac{x^2 - 2x - 3}{x}
$$

$$
\frac{x^2}{x} - \frac{2x}{x} - \frac{3}{x}
$$
$$
x - 2 - \frac{3}{x}
$$
The simplified expression is:
$$
\boxed{x - 2 - \frac{3}{x}}
$$

**b)** Simplify $8x^2 \times \frac{3xy}{6xy^2}$

$$
\frac{8x^2 \cdot 3xy}{6xy^2}
$$

$$
\frac{24x^3y}{6xy^2}
$$

$$
(x+1)(x-2) = x(x) + x(-2) + 1(x) + 1(-2)
$$
$$
= x^2 - 2x + x - 2
$$

$$
= x^2 - x - 2
$$
The expanded expression is:
$$
\boxed{x^2 - x - 2}
$$

**b)** Find the HCF of $4x^2y$ and $6xyz$

$$
4x^2y = 2^2 \cdot x^2 \cdot y
$$
$$
6xyz = 2 \cdot 3 \cdot x \cdot y \cdot z
$$

$$
\text{HCF} = 2 \cdot x \cdot y
$$
$$
\text{HCF} = 2xy
$$
The HCF is:
$$
\boxed{2xy}
$$