`(3)/(w)-(4)/(3)=(5w)/(10w^(2))`
In the equation above, what is the value of w?

Options

A. `(15)/(8)`
B. `(18)/(11)`
C. `(23)/(12)`
D. `(13)/(6)`

Answer

To solve the equation \(\frac{3}{w} - \frac{4}{3} = \frac{5w}{10w^2}\), we will follow these steps:

### Step 1: Simplify the Right Side
First, simplify the right side of the equation:
\[ \frac{5w}{10w^2} = \frac{5}{10w} = \frac{1}{2w} \]
Now, the equation becomes:
\[ \frac{3}{w} - \frac{4}{3} = \frac{1}{2w} \]

### Step 2: Eliminate the Fractions
To eliminate the fractions, we can multiply both sides of the equation by \(6w\) (the least common multiple of the denominators \(w\), \(3\), and \(2w\)):
\[ 6w \left(\frac{3}{w} - \frac{4}{3}\right) = 6w \cdot \frac{1}{2w} \]

### Step 3: Distribute on the Left Side
Distributing \(6w\) on the left side gives:
\[ 6w \cdot \frac{3}{w} - 6w \cdot \frac{4}{3} = 6 \cdot \frac{1}{2} \]
This simplifies to:
\[ 18 - 8w = 3 \]

### Step 4: Solve for \(w\)
Now, we will isolate \(w\):
1. Add \(8w\) to both sides:
\[ 18 = 3 + 8w \]
2. Subtract \(3\) from both sides:
\[ 15 = 8w \]
3. Divide both sides by \(8\):
\[ w = \frac{15}{8} \]

### Final Answer
Thus, the value of \(w\) is:
\[ \boxed{\frac{15}{8}} \]

---