1. **State the problem:** Simplify the algebraic fractions given: $$\frac{6x + 8}{2}, \quad \frac{7m - 70n^3}{7}, \quad \frac{9x^2 + 12x + 33}{6}, \quad \frac{8x^6 + x^4 + 3x}{x}$$ 2. **Recall the rule:** To simplify a fraction, divide each term in the numerator by the denominator. 3. **Simplify each fraction step-by-step:** **First fraction:** $$\frac{6x + 8}{2} = \frac{6x}{2} + \frac{8}{2}$$ $$= 3x + 4$$ **Second fraction:** $$\frac{7m - 70n^3}{7} = \frac{7m}{7} - \frac{70n^3}{7}$$ $$= m - 10n^3$$ **Third fraction:** $$\frac{9x^2 + 12x + 33}{6} = \frac{9x^2}{6} + \frac{12x}{6} + \frac{33}{6}$$ Simplify each term: $$= \frac{3 \cancel{3} x^2}{2 \cancel{3}} + 2x + \frac{11 \cancel{3}}{2 \cancel{3}} = \frac{3x^2}{2} + 2x + \frac{11}{2}$$ **Fourth fraction:** $$\frac{8x^6 + x^4 + 3x}{x} = \frac{8x^6}{x} + \frac{x^4}{x} + \frac{3x}{x}$$ $$= 8x^{6-1} + x^{4-1} + 3 = 8x^5 + x^3 + 3$$ 4. **Final simplified expressions:** $$3x + 4, \quad m - 10n^3, \quad \frac{3x^2}{2} + 2x + \frac{11}{2}, \quad 8x^5 + x^3 + 3$$ Each fraction is simplified by dividing numerator terms by the denominator, reducing coefficients and powers where applicable.