\( 1 \quad \frac { 2 a + 3 b } { 9 } + \frac { a - 4 b } { 6 } \)

Calculate or simplify the expression \( (2a+3b)/9+(a-4b)/6 \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(2a+3b\right)}{9}+\frac{\left(a-4b\right)}{6}\) - step1: Remove the parentheses: \(\frac{2a+3b}{9}+\frac{a-4b}{6}\) - step2: Reduce fractions to a common denominator: \(\frac{\left(2a+3b\right)\times 2}{9\times 2}+\frac{\left(a-4b\right)\times 3}{6\times 3}\) - step3: Multiply the numbers: \(\frac{\left(2a+3b\right)\times 2}{18}+\frac{\left(a-4b\right)\times 3}{6\times 3}\) - step4: Multiply the numbers: \(\frac{\left(2a+3b\right)\times 2}{18}+\frac{\left(a-4b\right)\times 3}{18}\) - step5: Transform the expression: \(\frac{\left(2a+3b\right)\times 2+\left(a-4b\right)\times 3}{18}\) - step6: Multiply the terms: \(\frac{4a+6b+\left(a-4b\right)\times 3}{18}\) - step7: Multiply the terms: \(\frac{4a+6b+3a-12b}{18}\) - step8: Calculate: \(\frac{7a-6b}{18}\) The simplified expression is \( \frac{7a-6b}{18} \).