Divide both sides by $ \sqrt{3} $:
["Divide Both Sides by √3: A Clear Guide to Simplifying Radical Expressions", "Divide both sides by $ \sqrt{3} $? Understanding how to simplify radical expressions is essential in algebra and higher mathematics. This step-by-step guide explains the process of dividing both sides of an equation by $ \sqrt{3} $, its implications, and how to simplify expressions involving square roots.", "---", "### What Does "Divide Both Sides by $ \sqrt{3} $" Mean?", "When solving equations involving square roots, it’s common to manipulate both sides to isolate variables or simplify radicals. Dividing both sides by $ \sqrt{3} $ means reducing every term on the equation by that same value. This operation preserves the equality and is often used when simplifying expressions such as:", "[\n\frac{f(x)}{\sqrt{3}} = g(x)\n]", "to isolate $ f(x) $ or $ g(x) $. However, dividing by $ \sqrt{3} $ requires care—especially when rationalizing expressions.", "---", "### Step-by-Step Process", "Step 1: Start with an equation involving $ \sqrt{3} $:", "[\na = b\sqrt{3}\n]", "Step 2: Divide both sides by $ \sqrt{3} $:", "[\n\frac{a}{\sqrt{3}} = b\n]", "Step 3: (Optional but common) Rationalize the denominator:", "Multiply numerator and denominator by $ \sqrt{3} $ to eliminate the radical in the denominator:", "[\n\frac{a \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{a\sqrt{3}}{3} = b\n]", "---", "### Example Problem", "Solve:\n[\n\frac{6}{\sqrt{3}} = x\sqrt{3}\n]", "Step 1:"]
