1) \( \frac{x}{3 x^{2} y}+\frac{x+1}{6 x y^{2}}-\frac{3}{9 x y} \)

Calculate or simplify the expression \( \frac{x}{3x^2y}+\frac{x+1}{6xy^2}-\frac{3}{9xy} \). Simplify the expression by following steps: - step0: Solution: \(\frac{x}{3x^{2}y}+\frac{x+1}{6xy^{2}}-\frac{3}{9xy}\) - step1: Divide the terms: \(\frac{1}{3xy}+\frac{x+1}{6xy^{2}}-\frac{3}{9xy}\) - step2: Calculate: \(\frac{1}{3xy}+\frac{x+1}{6xy^{2}}-\frac{1}{3xy}\) - step3: Reduce fractions to a common denominator: \(\frac{2y}{3xy\times 2y}+\frac{x+1}{6xy^{2}}-\frac{2y}{3xy\times 2y}\) - step4: Multiply the numbers: \(\frac{2y}{6xy\times y}+\frac{x+1}{6xy^{2}}-\frac{2y}{3xy\times 2y}\) - step5: Multiply the numbers: \(\frac{2y}{6xy\times y}+\frac{x+1}{6xy^{2}}-\frac{2y}{6xy\times y}\) - step6: Multiply the terms: \(\frac{2y}{6xy^{2}}+\frac{x+1}{6xy^{2}}-\frac{2y}{6xy\times y}\) - step7: Multiply the terms: \(\frac{2y}{6xy^{2}}+\frac{x+1}{6xy^{2}}-\frac{2y}{6xy^{2}}\) - step8: Transform the expression: \(\frac{2y+x+1-2y}{6xy^{2}}\) - step9: Calculate: \(\frac{x+1}{6xy^{2}}\) La expresión simplificada es \( \frac{x+1}{6xy^{2}} \).