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. \( \frac{3}{x^{3}}-\frac{2}{x^{2}}-\frac{1}{x} \)

To simplify the expressions, you can tackle them one by one: 1. For \( \frac{x-3}{3}-\frac{x-2}{2} \), first find a common denominator, which is 6. Rewrite each term: \[ \frac{2(x-3)}{6} - \frac{3(x-2)}{6} = \frac{2x - 6 - 3x + 6}{6} = \frac{-x}{6} = -\frac{x}{6}. \] 2. For \( 30 \frac{3}{2 x}-\frac{2}{3 x}-\frac{1}{4 x} \), first factor out \( \frac{1}{x} \): \[ \frac{1}{x} \left( 30 \cdot \frac{3}{2} - \frac{2}{3} - \frac{1}{4} \right) = \frac{1}{x} \left( 45 - \frac{2}{3} - \frac{1}{4} \right). \] To combine the constants, find a common denominator of 12: \[ = \frac{1}{x} \left( \frac{540}{12} - \frac{8}{12} - \frac{3}{12} \right) = \frac{1}{x} \left( \frac{529}{12} \right) = \frac{529}{12x}. \] 5. For \( \frac{3}{x^{3}}-\frac{2}{x^{2}}-\frac{1}{x} \), rewrite with a common denominator of \( x^3 \): \[ \frac{3 - 2x - x^2}{x^3} = \frac{-x^2 - 2x + 3}{x^3}. \] You can rearrange it to have a clearer look: \[ \frac{-(x^2 + 2x - 3)}{x^3} = \frac{-(x+3)(x-1)}{x^3}. \] Final simplified results: 1. \( -\frac{x}{6} \) 2. \( \frac{529}{12x} \) 3. \( \frac{-(x+3)(x-1)}{x^3} \)