Divide `(5x^(2)+6xy)` by x.

Options

A. `5x+6y`
B. `5x-6y`
C. `5x^(3)+6x^(2)y`
D. None of these

Answer

To divide the expression \(5x^2 + 6xy\) by \(x\), we can follow these steps:

### Step 1: Write the expression in a division format
We start with the expression:
\[ 5x^2 + 6xy \]
We want to divide this by \(x\):
\[ \frac{5x^2 + 6xy}{x} \]

### Step 2: Apply the property of division
According to the property of division, we can separate the terms in the numerator:
\[ \frac{5x^2}{x} + \frac{6xy}{x} \]

### Step 3: Simplify each term
Now, we simplify each term separately:
1. For the first term:
\[ \frac{5x^2}{x} = 5x^{2-1} = 5x \]
2. For the second term:
\[ \frac{6xy}{x} = 6y \cdot \frac{x}{x} = 6y \]

### Step 4: Combine the simplified terms
Now, we combine the simplified terms:
\[ 5x + 6y \]

### Final Answer
Thus, the result of dividing \(5x^2 + 6xy\) by \(x\) is:
\[ \boxed{5x + 6y} \]

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