Solve : `(y+2)/(4)-(y-3)/(3)=(1)/(2)`

Answer

To solve the equation \(\frac{y+2}{4} - \frac{y-3}{3} = \frac{1}{2}\), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM)
The denominators in the equation are 4, 3, and 2. The LCM of these numbers is 12.

### Step 2: Multiply through by the LCM
Multiply every term in the equation by 12 to eliminate the fractions:

\[ 12 \cdot \left(\frac{y+2}{4}\right) - 12 \cdot \left(\frac{y-3}{3}\right) = 12 \cdot \left(\frac{1}{2}\right) \]

This simplifies to:

\[ 3(y + 2) - 4(y - 3) = 6 \]

### Step 3: Distribute the terms
Now, distribute the 3 and -4 across the terms in the parentheses:

\[ 3y + 6 - 4y + 12 = 6 \]

### Step 4: Combine like terms
Combine the \(y\) terms and the constant terms:

\[ (3y - 4y) + (6 + 12) = 6 \]

This simplifies to:

\[ -y + 18 = 6 \]

### Step 5: Isolate the variable
To isolate \(y\), subtract 18 from both sides:

\[ -y = 6 - 18 \]

This simplifies to:

\[ -y = -12 \]

### Step 6: Solve for \(y\)
Multiply both sides by -1 to solve for \(y\):

\[ y = 12 \]

### Final Answer
The solution to the equation is:

\[ y = 12 \]

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