For all `y ne 0, (1)/(y)+(1)/(2y)+(1)/(3y) =`

Options

A. `(1)/(2y)`
B. `(1)/(6y)`
C. `(5)/(6y)`
D. `(11)/(6y)`

Explanation

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

### Step 1: Find a common denominator
The denominators are \( y \), \( 2y \), and \( 3y \). The least common multiple (LCM) of these denominators is \( 6y \).

### Step 2: Rewrite each fraction with the common denominator
We will rewrite each term with the common denominator \( 6y \):
- \( \frac{1}{y} = \frac{6}{6y} \)
- \( \frac{1}{2y} = \frac{3}{6y} \)
- \( \frac{1}{3y} = \frac{2}{6y} \)

### Step 3: Combine the fractions
Now we can combine the fractions:
\[ \frac{6}{6y} + \frac{3}{6y} + \frac{2}{6y} = \frac{6 + 3 + 2}{6y} = \frac{11}{6y} \]

### Step 4: Write the final answer
Thus, the value of \( \frac{1}{y} + \frac{1}{2y} + \frac{1}{3y} \) is:
\[ \frac{11}{6y} \]