1. **State the problem:** Subtract fractions with unlike denominators, such as $$\frac{3x}{4x} - \frac{1x}{2x}$$. 2. **Formula and rule:** To subtract fractions with different denominators, first find a common denominator by multiplying the denominators together or finding the least common multiple (LCM). Then, convert each fraction to an equivalent fraction with the common denominator. 3. **Example a:** $$\frac{3x}{4x} - \frac{1x}{2x}$$ - Find common denominator: $$4x \times 2x = 8x^2$$ - Convert fractions: $$\frac{3x}{4x} = \frac{3x \times 2x}{4x \times 2x} = \frac{6x^2}{8x^2}$$ $$\frac{1x}{2x} = \frac{1x \times 4x}{2x \times 4x} = \frac{4x^2}{8x^2}$$ - Subtract numerators: $$\frac{6x^2}{8x^2} - \frac{4x^2}{8x^2} = \frac{6x^2 - 4x^2}{8x^2} = \frac{2x^2}{8x^2}$$ - Simplify by canceling common factors: $$\frac{\cancel{2}x^2}{\cancel{8}x^2} = \frac{1}{4}$$ 4. **Explanation:** We multiply numerator and denominator to get the same denominator, then subtract numerators and simplify. 5. **Final answer for a:** $$\frac{1}{4}$$ This method applies similarly to all other fraction subtraction problems with unlike denominators.