EXERCISE 18 Fully simplify each of the following expressions. \( \begin{array}{ll}\text { 1. } \frac{x-3}{3}-\frac{x+2}{4} & \text { 2. } \frac{2 x-1}{3} \\ \text { 3. } \frac{2}{5} x+\frac{3}{4} x-\frac{1}{2} x & \text { 4. } \frac{2 x+3}{5} \\ \text { 5. } 1-\frac{x}{3}-\frac{x+2}{6} & \text { 6. } \frac{3}{2}-\frac{x}{3} \\ \text { 7. } \frac{5 x-3}{2}-\frac{x-7}{5} & \text { 8. } \frac{x}{2}-3 x \\ \text { 9. } \frac{2 x+3}{5}-\frac{3 x-2}{6} & \text { 10. } x^{2}-\frac{2}{3} \\ \text { 11. } \frac{2}{3} a-\frac{3}{2} b+1 & \text { 12. } \frac{4}{3}-\frac{m}{2} \\ \text { 13. } \frac{2 x-3}{} \text { 3x-2 } & \text { l }\end{array} \)

1. To simplify \(\frac{x-3}{3}-\frac{x+2}{4}\), first find a common denominator, which is 12. Rewrite the fractions: \(\frac{4(x-3)}{12} - \frac{3(x+2)}{12}\). Now, combine the numerators: \(\frac{4x - 12 - 3x - 6}{12}\). This gives \(\frac{x - 18}{12}\), which simplifies to \(\frac{x}{12} - \frac{3}{2}\). 2. The expression \(\frac{2 x-1}{3}\) is already in a simple form. However, if you're looking to further simplify or rewrite it, you could distribute or factor out a common factor as needed. Just note that any direct transformations will still yield the simplest linear representation in this case, which can be helpful for various applications, like substituting values in equations or integrating into more complex functions.