c) \( \frac{a}{2}-\frac{a+3}{10}+\frac{a-1}{5} \)

Simplify the expression by following steps: - step0: Solution: \(\frac{a}{2}-\frac{a+3}{10}+\frac{a-1}{5}\) - step1: Reduce fractions to a common denominator: \(\frac{a\times 5}{2\times 5}-\frac{a+3}{10}+\frac{\left(a-1\right)\times 2}{5\times 2}\) - step2: Multiply the numbers: \(\frac{a\times 5}{10}-\frac{a+3}{10}+\frac{\left(a-1\right)\times 2}{5\times 2}\) - step3: Multiply the numbers: \(\frac{a\times 5}{10}-\frac{a+3}{10}+\frac{\left(a-1\right)\times 2}{10}\) - step4: Transform the expression: \(\frac{a\times 5-\left(a+3\right)+\left(a-1\right)\times 2}{10}\) - step5: Reorder the terms: \(\frac{5a-\left(a+3\right)+\left(a-1\right)\times 2}{10}\) - step6: Multiply the terms: \(\frac{5a-\left(a+3\right)+2a-2}{10}\) - step7: Calculate: \(\frac{6a-5}{10}\) To simplify the expression \( \frac{a}{2} - \frac{a+3}{10} + \frac{a-1}{5} \), we can follow these steps: 1. **Identify a common denominator**: The denominators are 2, 10, and 5. The least common multiple (LCM) of these numbers is 10. 2. **Rewrite each term with the common denominator**: - The first term \( \frac{a}{2} \) can be rewritten as \( \frac{5a}{10} \). - The second term \( -\frac{a+3}{10} \) remains as is. - The third term \( \frac{a-1}{5} \) can be rewritten as \( \frac{2(a-1)}{10} = \frac{2a - 2}{10} \). 3. **Combine the terms**: \[ \frac{5a}{10} - \frac{a+3}{10} + \frac{2a - 2}{10} = \frac{5a - (a + 3) + (2a - 2)}{10} \] 4. **Simplify the numerator**: \[ 5a - a - 3 + 2a - 2 = 6a - 5 \] 5. **Final expression**: \[ \frac{6a - 5}{10} \] Thus, the simplified form of the expression is \( \frac{6a - 5}{10} \).