1. Stating the problem: Simplify the expression $\frac{3}{4} + \frac{1}{2} - \frac{1}{8}$.\n\n2. Find a common denominator for the fractions. The denominators are 4, 2, and 8. The least common denominator (LCD) is 8.\n\n3. Convert each fraction to have denominator 8:\n$$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$$\n$$\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}$$\n$$\frac{1}{8} = \frac{1}{8}$$\n\n4. Substitute back into the expression:\n$$\frac{6}{8} + \frac{4}{8} - \frac{1}{8}$$\n\n5. Combine the numerators since denominators are the same:\n$$\frac{6 + 4 - 1}{8} = \frac{9}{8}$$\n\n6. The fraction $\frac{9}{8}$ is an improper fraction and can be written as a mixed number:\n$$1 \frac{1}{8}$$\n\nFinal answer: $\frac{9}{8}$ or $1 \frac{1}{8}$.