Subtract. \[ \frac{13 b+2}{8 b}-\frac{3 b}{8 b} \] Simplify your answer as much as possional expressions with common de Sims

Simplify the expression by following steps: - step0: Solution: \(\frac{\left(13b+2\right)}{8b}-\frac{3b}{8b}\) - step1: Remove the parentheses: \(\frac{13b+2}{8b}-\frac{3b}{8b}\) - step2: Transform the expression: \(\frac{13b+2-3b}{8b}\) - step3: Subtract the terms: \(\frac{10b+2}{8b}\) - step4: Factor: \(\frac{2\left(5b+1\right)}{8b}\) - step5: Reduce the fraction: \(\frac{5b+1}{4b}\) To subtract the two fractions: \[ \frac{13b + 2}{8b} - \frac{3b}{8b} \] we can combine them since they have a common denominator of \(8b\): 1. **Combine the numerators**: \[ \frac{(13b + 2) - 3b}{8b} \] 2. **Simplify the numerator**: \[ 13b + 2 - 3b = 10b + 2 \] 3. **Write the combined fraction**: \[ \frac{10b + 2}{8b} \] 4. **Factor the numerator**: \[ \frac{2(5b + 1)}{8b} \] 5. **Simplify the fraction**: \[ \frac{2(5b + 1)}{8b} = \frac{5b + 1}{4b} \] Thus, the simplified result is: \[ \frac{5b + 1}{4b} \]