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📅 July 7, 2026 👤 scraface

Jul 07, 2026

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Evaluate the limit \(\lim_{x \to 3} \frac{x^2 - 9}{x - 3}\).
Factor the numerator: \(\frac{(x - 3)(x + 3)}{x - 3}\).
Cancel the common factor: \(\lim_{x \to 3} (x + 3)\).
Substitute \(x = 3\): \(3 + 3 = 6\).
Solve the system of equations: \(2x + 3y = 12\) and \(x - y = 3\).
Solve the second equation for \(x\): \(x = y + 3\).
Substitute into the first equation: \(2(y + 3) + 3y = 12\).
Simplify: \(2y + 6 + 3y = 12\), \(5y + 6 = 12\), \(5y = 6\).
Divide by 5: \(y = \frac{6}{5}\).
Substitute back: \(x = \frac{6}{5} + 3 = \frac{21}{5}\).

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