Let's simplify the expression \(\frac{6\sqrt{x} + 1}{2\sqrt{x}}\).

We can split the fraction into two separate terms:

\[
\frac{6\sqrt{x}}{2\sqrt{x}} + \frac{1}{2\sqrt{x}}
\]

Simplifying each term separately:

1. \(\frac{6\sqrt{x}}{2\sqrt{x}} = \frac{6}{2} = 3\) (since \(\sqrt{x}\) cancels out).
2. \(\frac{1}{2\sqrt{x}}\) remains as it is.

So, the simplified expression is:

\[
3 + \frac{1}{2\sqrt{x}}
\]

Would you like further details on this simplification, or do you have any other questions?

Here are 5 related questions to consider:

1. How do you simplify expressions with radicals in both the numerator and denominator?
2. What are the rules for simplifying expressions involving square roots?
3. How can you rationalize a denominator with a square root?
4. How do you handle algebraic fractions with more complex expressions?
5. What is the process for adding or subtracting fractions with radicals?

**Tip:** When simplifying expressions, always look for common factors that can be canceled to make the expression simpler.

Discover how to simplify the radical expression (6sqrt(x) + 1)/(2sqrt(x)) with detailed steps. This problem focuses on key algebraic techniques such as splitting fractions and simplifying radicals, making it ideal for students in Grades 8-10.

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