Write `(w)/(2)-(w)/(3)` as a single fraction.

Answer

To write \(\frac{w}{2} - \frac{w}{3}\) as a single fraction, follow these steps:

### Step 1: Identify the denominators
The denominators of the fractions are 2 and 3.

### Step 2: Find the Least Common Multiple (LCM)
The LCM of 2 and 3 is 6. This will be the common denominator for the fractions.

### Step 3: Rewrite each fraction with the common denominator
We need to express both fractions with the denominator of 6:
- For \(\frac{w}{2}\), we can multiply the numerator and denominator by 3:
\[ \frac{w}{2} = \frac{w \cdot 3}{2 \cdot 3} = \frac{3w}{6} \]
- For \(\frac{w}{3}\), we can multiply the numerator and denominator by 2:
\[ \frac{w}{3} = \frac{w \cdot 2}{3 \cdot 2} = \frac{2w}{6} \]

### Step 4: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{3w}{6} - \frac{2w}{6} = \frac{3w - 2w}{6} \]

### Step 5: Simplify the numerator
Now simplify the numerator:
\[ 3w - 2w = w \]
So we have:
\[ \frac{3w - 2w}{6} = \frac{w}{6} \]

### Final Answer
Thus, \(\frac{w}{2} - \frac{w}{3}\) as a single fraction is:
\[ \frac{w}{6} \]

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