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Home » \[ f''(x) = racddx(12x^2 - 18x + 6) = 24x - 18. \] - Veritas Home Health

\[ f''(x) = racddx(12x^2 - 18x + 6) = 24x - 18. \] - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 rac{x+3}{x-2} - 4 < 0.

📌 Write the left-hand side as a single rational expression:

📌 rac{x+3 - 4(x - 2)}{x - 2} = rac{x+3 - 4x + 8}{x - 2} = rac{-3x + 11}{x - 2}.

📌 So the inequality becomes:

📌 rac{-3x + 11}{x - 2} < 0.

📌 We analyze the sign of this rational expression by identifying the critical points where the numerator or denominator is zero:

📌 Numerator zero: $ -3x + 11 = 0 \Rightarrow x = rac{11}{3} $.

📌 Denominator zero: $ x - 2 = 0 \Rightarrow x = 2 $.

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