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Home » Question: Rationalize the denominator of $ \frac{\sqrt7}{\sqrt7 - \sqrt3} $. - 500apps

Question: Rationalize the denominator of $ \frac{\sqrt7}{\sqrt7 - \sqrt3} $. - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 y - 2 = -\frac{4}{3}(x - 1)

📌 \Rightarrow y = -\frac{4}{3}x + \frac{4}{3} + 2 = -\frac{4}{3}x + \frac{10}{3}

📌 Now find intersection with original line \( 3x - 4y + 12 = 0 \).

📌 Substitute \( y = -\frac{4}{3}x + \frac{10}{3} \):

📌 3x - 4\left(-\frac{4}{3}x + \frac{10}{3}\right) + 12 = 0

📌 \Rightarrow 3x + \frac{16}{3}x - \frac{40}{3} + 12 = 0

📌 Multiply through by 3:

📌 9x + 16x - 40 + 36 = 0 \Rightarrow 25x - 4 = 0 \Rightarrow x = \frac{4}{25}

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