TEST 2 Simplify: 1. \( \frac{x-3}{3}-\frac{x-2}{2} \) \( 30 \frac{3}{2 x}-\frac{2}{3 x}-\frac{1}{4 x} \) 5. \( \frac{3}{x^{3}}-\frac{2}{x^{2}}-\frac{1}{x} \)

Calculate or simplify the expression \( (x-3)/3-(x-2)/2 \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(x-3\right)}{3}-\frac{\left(x-2\right)}{2}\) - step1: Remove the parentheses: \(\frac{x-3}{3}-\frac{x-2}{2}\) - step2: Reduce fractions to a common denominator: \(\frac{\left(x-3\right)\times 2}{3\times 2}-\frac{\left(x-2\right)\times 3}{2\times 3}\) - step3: Multiply the numbers: \(\frac{\left(x-3\right)\times 2}{6}-\frac{\left(x-2\right)\times 3}{2\times 3}\) - step4: Multiply the numbers: \(\frac{\left(x-3\right)\times 2}{6}-\frac{\left(x-2\right)\times 3}{6}\) - step5: Transform the expression: \(\frac{\left(x-3\right)\times 2-\left(x-2\right)\times 3}{6}\) - step6: Multiply the terms: \(\frac{2x-6-\left(x-2\right)\times 3}{6}\) - step7: Multiply the terms: \(\frac{2x-6-\left(3x-6\right)}{6}\) - step8: Subtract the terms: \(\frac{-x}{6}\) - step9: Rewrite the fraction: \(-\frac{x}{6}\) Calculate or simplify the expression \( 30*3/2*x-2/3*x-1/4*x \). Simplify the expression by following steps: - step0: Solution: \(\frac{30\times 3}{2}x-\frac{2}{3}x-\frac{1}{4}x\) - step1: Reduce the fraction: \(45x-\frac{2}{3}x-\frac{1}{4}x\) - step2: Collect like terms: \(\left(45-\frac{2}{3}-\frac{1}{4}\right)x\) - step3: Subtract the numbers: \(\frac{529}{12}x\) Calculate or simplify the expression \( 3/x^3-2/x^2-1/x \). Simplify the expression by following steps: - step0: Solution: \(\frac{3}{x^{3}}-\frac{2}{x^{2}}-\frac{1}{x}\) - step1: Reduce fractions to a common denominator: \(\frac{3}{x^{3}}-\frac{2x}{x^{2}\times x}-\frac{x\times x}{x\times x\times x}\) - step2: Multiply: \(\frac{3}{x^{3}}-\frac{2x}{x^{3}}-\frac{x\times x}{x\times x\times x}\) - step3: Multiply: \(\frac{3}{x^{3}}-\frac{2x}{x^{3}}-\frac{x\times x}{x^{3}}\) - step4: Transform the expression: \(\frac{3-2x-x\times x}{x^{3}}\) - step5: Multiply the terms: \(\frac{3-2x-x^{2}}{x^{3}}\) The simplified expressions are: 1. \( \frac{x-3}{3}-\frac{x-2}{2} = -\frac{x}{6} \) 2. \( 30 \frac{3}{2 x}-\frac{2}{3 x}-\frac{1}{4 x} = \frac{529}{12}x \) 3. \( \frac{3}{x^{3}}-\frac{2}{x^{2}}-\frac{1}{x} = \frac{3-2x-x^{2}}{x^{3}} \)