1. **State the problem:** Simplify the expression $$\frac{5x}{3x^2} - \frac{7}{6x}$$. 2. **Find a common denominator:** The denominators are $3x^2$ and $6x$. The least common denominator (LCD) is $6x^2$. 3. **Rewrite each fraction with the LCD:** $$\frac{5x}{3x^2} = \frac{5x \times 2}{3x^2 \times 2} = \frac{10x}{6x^2}$$ $$\frac{7}{6x} = \frac{7 \times x}{6x \times x} = \frac{7x}{6x^2}$$ 4. **Subtract the numerators over the common denominator:** $$\frac{10x}{6x^2} - \frac{7x}{6x^2} = \frac{10x - 7x}{6x^2} = \frac{3x}{6x^2}$$ 5. **Simplify the fraction:** $$\frac{3x}{6x^2} = \frac{3}{6} \times \frac{x}{x^2} = \frac{1}{2} \times \frac{1}{x} = \frac{1}{2x}$$ **Final answer:** $$\frac{1}{2x}$$ which corresponds to option A.