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Home » What Happened Inside This Penny Arcade Made Local Gamers Go Viral! - Carbonext

What Happened Inside This Penny Arcade Made Local Gamers Go Viral! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 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 \( \boxed{2(\sqrt{5} + \sqrt{3})} \).

📌 Find the value of \( x \) that satisfies \( \log_2(x^2 - 4) = 3 \).

📌 Start by rewriting the logarithmic equation in exponential form:

📌 \[ \log_2(x^2 - 4) = 3 \Rightarrow x^2 - 4 = 2^3 = 8. \]

📌 Solve for \( x^2 \):

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