In the expression `(6/5)/(12/(2y)-5/y)=1`, What is the value of y?

Options

A. `45/6`
B. 35/9
C. 45/9
D. 60/3

Answer

To solve the equation \((\frac{6}{5})/(\frac{12}{2y}-\frac{5}{y})=1\), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{6/5}{\frac{12}{2y} - \frac{5}{y}} = 1 \]

### Step 2: Multiply both sides by the denominator
To eliminate the fraction, we can multiply both sides by \(\left(\frac{12}{2y} - \frac{5}{y}\right)\):
\[ \frac{6}{5} = \frac{12}{2y} - \frac{5}{y} \]

### Step 3: Find a common denominator for the right side
The common denominator for \(\frac{12}{2y}\) and \(\frac{5}{y}\) is \(2y\). We rewrite the right side:
\[ \frac{12}{2y} - \frac{5}{y} = \frac{12 - 10}{2y} = \frac{2}{2y} = \frac{1}{y} \]

### Step 4: Set the equation
Now we have:
\[ \frac{6}{5} = \frac{1}{y} \]

### Step 5: Cross-multiply to solve for \(y\)
Cross-multiplying gives us:
\[ 6y = 5 \]

### Step 6: Solve for \(y\)
Now, divide both sides by 6:
\[ y = \frac{5}{6} \]

### Final Answer
Thus, the value of \(y\) is:
\[ \boxed{\frac{5}{6}} \]