Rationalize Denominator 356724

1. **State the problem:** Rationalize the denominator of the expression $$\frac{\sqrt{g}}{\sqrt{g} + \sqrt{k}}$$ where $g$ and $k$ are positive real numbers. 2. **Recall the formula:** To rationalize a denominator of the form $a + b$, multiply numerator and denominator by the conjugate $a - b$ to use the difference of squares formula: $$(a + b)(a - b) = a^2 - b^2$$ 3. **Apply the conjugate:** Multiply numerator and denominator by $$\sqrt{g} - \sqrt{k}$$: $$\frac{\sqrt{g}}{\sqrt{g} + \sqrt{k}} \times \frac{\sqrt{g} - \sqrt{k}}{\sqrt{g} - \sqrt{k}} = \frac{\sqrt{g}(\sqrt{g} - \sqrt{k})}{(\sqrt{g} + \sqrt{k})(\sqrt{g} - \sqrt{k})}$$ 4. **Simplify numerator:** $$\sqrt{g} \times \sqrt{g} - \sqrt{g} \times \sqrt{k} = g - \sqrt{g}\sqrt{k}$$ 5. **Simplify denominator using difference of squares:** $$(\sqrt{g})^2 - (\sqrt{k})^2 = g - k$$ 6. **Write the expression:** $$\frac{g - \sqrt{g}\sqrt{k}}{g - k}$$ 7. **Final answer:** $$\frac{g - \sqrt{g}\sqrt{k}}{g - k}$$ This is the rationalized form of the original expression.