1. Stating the problem: Simplify the expression $$\frac{3}{4x} - \frac{5}{6x^2}$$. 2. Find the common denominator: The denominators are $$4x$$ and $$6x^2$$. The least common denominator (LCD) is $$12x^2$$ because $$12$$ is the least common multiple of $$4$$ and $$6$$, and $$x^2$$ is the highest power of $$x$$. 3. Rewrite each fraction with the LCD: $$\frac{3}{4x} = \frac{3 \times 3x}{4x \times 3x} = \frac{9x}{12x^2}$$ $$\frac{5}{6x^2} = \frac{5 \times 2}{6x^2 \times 2} = \frac{10}{12x^2}$$ 4. Perform the subtraction: $$\frac{9x}{12x^2} - \frac{10}{12x^2} = \frac{9x - 10}{12x^2}$$ 5. Final simplified expression: $$\boxed{\frac{9x - 10}{12x^2}}$$ This is the simplest form unless further factoring is possible, which is not in this case.