1. SOLUTION:
[tex]\begin{aligned} \left(\frac{f}{g}\right)(x) & = \frac{f(x)}{g(x)} \\ & = \frac{8x^3 + 6x^2}{2x} \\ & = \frac{2x^2(4x + 3)}{2x} \\ & = x(4x + 3) \\ & = \boxed{4x^2 + 3x} \end{aligned}[/tex]
2. SOLUTION:
[tex]\begin{aligned} \left(\frac{f}{g}\right)(x) & = \frac{f(x)}{g(x)} \\ & = \frac{-24x^3 + 32x^2}{8x} \\ & = \frac{-8x^2(3x - 4)}{8x} \\ & = -x(3x - 4) \\ & = \boxed{-3x^2 + 4x} \end{aligned}[/tex]
3. SOLUTION:
[tex]\begin{aligned} (f \cdot g)(x) & = f(x) \cdot g(x) \\ & = (4x - 3)(-2x) \\ & = \boxed{-8x^2 + 6x} \end{aligned}[/tex]
4. SOLUTION:
[tex]\begin{aligned} (f \cdot g)(x) & = f(x) \cdot g(x) \\ & = (6x - 2)(-5x) \\ & = \boxed{-30x^2 + 10x} \end{aligned}[/tex]
5. SOLUTION:
[tex]\begin{aligned} (f + g)(x) & = f(x) + g(x) \\ & = (4x + 8) + (2x + 3) \\ & = 4x + 2x + 8 + 3 \\ & = \boxed{6x + 11} \end{aligned}[/tex]
