What the simplified value of `2sqrt3-1/sqrt3` ?

Options

A. a. `5sqrt3`
B. b. `5/sqrt3`
C. c. `3sqrt5`
D. d. `3/sqrt5`

Answer

To simplify the expression \( \frac{2\sqrt{3} - 1}{\sqrt{3}} \), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ \frac{2\sqrt{3} - 1}{\sqrt{3}} \]

### Step 2: Split the fraction
We can separate the terms in the numerator:
\[ \frac{2\sqrt{3}}{\sqrt{3}} - \frac{1}{\sqrt{3}} \]

### Step 3: Simplify each term
1. For the first term:
\[ \frac{2\sqrt{3}}{\sqrt{3}} = 2 \]
2. For the second term, we can rationalize the denominator:
\[ \frac{1}{\sqrt{3}} = \frac{1 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{3}}{3} \]

### Step 4: Combine the simplified terms
Now we can combine the simplified terms:
\[ 2 - \frac{\sqrt{3}}{3} \]

### Step 5: Find a common denominator
To combine these terms, we need a common denominator, which is 3:
\[ 2 = \frac{6}{3} \]
Thus, we have:
\[ \frac{6}{3} - \frac{\sqrt{3}}{3} = \frac{6 - \sqrt{3}}{3} \]

### Final Result
The simplified value of \( \frac{2\sqrt{3} - 1}{\sqrt{3}} \) is:
\[ \frac{6 - \sqrt{3}}{3} \]