Solve :
`x-(x-1)/(2)=1-(x-2)/(3)`

Answer

To solve the equation \( x - \frac{x-1}{2} = 1 - \frac{x-2}{3} \), follow these steps:

1. **Write the given equation:**
\[ x - \frac{x-1}{2} = 1 - \frac{x-2}{3} \]

2. **Make the denominators the same:**
- The denominators are 2 and 3. The least common multiple (LCM) of 2 and 3 is 6.
- Multiply both sides by 6 to eliminate the denominators.

\[ 6 \left( x - \frac{x-1}{2} \right) = 6 \left( 1 - \frac{x-2}{3} \right) \]

3. **Distribute 6 to each term inside the parentheses:**
\[ 6x - 6 \cdot \frac{x-1}{2} = 6 \cdot 1 - 6 \cdot \frac{x-2}{3} \]

4. **Simplify each term:**
- \( 6 \cdot \frac{x-1}{2} = 3(x-1) \)
- \( 6 \cdot \frac{x-2}{3} = 2(x-2) \)

So, the equation becomes:
\[ 6x - 3(x-1) = 6 - 2(x-2) \]

5. **Distribute and simplify:**
\[ 6x - 3x + 3 = 6 - 2x + 4 \]

6. **Combine like terms:**
\[ 3x + 3 = 10 - 2x \]

7. **Move all terms involving \( x \) to one side and constants to the other side:**
\[ 3x + 2x = 10 - 3 \]

8. **Combine like terms:**
\[ 5x = 7 \]

9. **Solve for \( x \):**
\[ x = \frac{7}{5} \]

So, the solution to the equation is:
\[ x = \frac{7}{5} \]