Solve `(gamma +2)/( 3) + ( gamma +3)/(2) = gamma + 1`

Answer

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

### Step 1: Find a common denominator
The denominators in the equation are 3 and 2. The least common multiple (LCM) of 3 and 2 is 6. We will multiply each term by 6 to eliminate the denominators.

\[ 6 \left(\frac{\gamma + 2}{3}\right) + 6 \left(\frac{\gamma + 3}{2}\right) = 6(\gamma + 1) \]

### Step 2: Simplify each term
Now, we simplify each term:

\[ 2(\gamma + 2) + 3(\gamma + 3) = 6(\gamma + 1) \]

### Step 3: Distribute
Next, we distribute the terms:

\[ 2\gamma + 4 + 3\gamma + 9 = 6\gamma + 6 \]

### Step 4: Combine like terms
Now, we combine the like terms on the left side:

\[ (2\gamma + 3\gamma) + (4 + 9) = 6\gamma + 6 \]

This simplifies to:

\[ 5\gamma + 13 = 6\gamma + 6 \]

### Step 5: Rearrange the equation
Now, we will move all terms involving \(\gamma\) to one side and constant terms to the other side:

\[ 5\gamma - 6\gamma = 6 - 13 \]

### Step 6: Simplify both sides
This simplifies to:

\[ -\gamma = -7 \]

### Step 7: Solve for \(\gamma\)
Now, we can solve for \(\gamma\):

\[ \gamma = 7 \]

### Final Answer
Thus, the solution to the equation is:

\[ \gamma = 7 \]

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