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captain james t. kirk - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 \( a + b = 7 \)

📌 Substitute equation (2) into equation (1):

📌 \[ a \cdot 7 = 20 \Rightarrow 7a = 20 \Rightarrow a = \frac{20}{7}. \]

📌 Thus, the value of \( a \) is \( \boxed{\frac{20}{7}} \).

📌 Rationalize the denominator of \( \frac{4}{\sqrt{5} - \sqrt{3}} \).

📌 To rationalize the denominator, multiply numerator and denominator by the conjugate \( \sqrt{5} + \sqrt{3} \):

📌 \frac{4}{\sqrt{5} - \sqrt{3}} \cdot \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}} = \frac{4(\sqrt{5} + \sqrt{3})}{(\sqrt{5})^2 - (\sqrt{3})^2} = \frac{4(\sqrt{5} + \sqrt{3})}{5 - 3} = \frac{4(\sqrt{5} + \sqrt{3})}{2} = 2(\sqrt{5} + \sqrt{3}).

📌 Thus, the rationalized expression is \( \boxed{2(\sqrt{5} + \sqrt{3})} \).

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