Find the value of `( 8x + 6y ^(2)) div 2y.`

Options

A. `4x + 3y`
B. `4 ((x)/(y)) + 3y`
C. `8x + 3y`
D. None of these

Answer

To find the value of \( \frac{8x + 6y^2}{2y} \), we will simplify the expression step by step.

### Step 1: Write the expression
We start with the expression:
\[ \frac{8x + 6y^2}{2y} \]

### Step 2: Split the fraction
We can separate the terms in the numerator:
\[ \frac{8x}{2y} + \frac{6y^2}{2y} \]

### Step 3: Simplify the first term
Now, simplify the first term \( \frac{8x}{2y} \):
\[ \frac{8}{2} \cdot \frac{x}{y} = 4 \cdot \frac{x}{y} = \frac{4x}{y} \]

### Step 4: Simplify the second term
Next, simplify the second term \( \frac{6y^2}{2y} \):
\[ \frac{6}{2} \cdot \frac{y^2}{y} = 3 \cdot y = 3y \]

### Step 5: Combine the simplified terms
Now, combine the simplified terms:
\[ \frac{4x}{y} + 3y \]

### Final Result
Thus, the simplified expression is:
\[ \frac{4x}{y} + 3y \]