Questions: Simplify. Assume that all variables represent positive real numbers. √(3x) - √(x)/√(3) A. -1/3 B. 0 C. 2√(3x)/3 D. √(3x)/3

Solution Steps

To simplify the given expression, we need to combine the terms under a common denominator and then simplify the resulting expression.

Given the expression: \[ \sqrt{3x} - \frac{\sqrt{x}}{\sqrt{3}} \]

First, rewrite \(\frac{\sqrt{x}}{\sqrt{3}}\) as \(\frac{\sqrt{3x}}{3}\): \[ \sqrt{3x} - \frac{\sqrt{3x}}{3} \]

Combine the terms under a common denominator: \[ \sqrt{3x} - \frac{\sqrt{3x}}{3} = \frac{3\sqrt{3x}}{3} - \frac{\sqrt{3x}}{3} = \frac{3\sqrt{3x} - \sqrt{3x}}{3} \]

Simplify the numerator: \[ 3\sqrt{3x} - \sqrt{3x} = 2\sqrt{3x} \]

Simplify the fraction: \[ \frac{2\sqrt{3x}}{3} \]

Final Answer