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Home » Unlock Spanish Faster: The Ultimate Guide to Mastering Cognates! - American Beagle Club

Unlock Spanish Faster: The Ultimate Guide to Mastering Cognates! - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 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 $.

📌 These divide the real line into intervals:

📌 We test the sign of $ rac{-3x + 11}{x - 2} $ in each interval:

📌 For $ x < 2 $, say $ x = 0 $: numerator $ -3(0) + 11 = 11 > 0 $, denominator $ 0 - 2 = -2 < 0 $ â negative.

📌 For $ 2 < x < rac{11}{3} $, say $ x = 3 $: numerator $ -9 + 11 = 2 > 0 $, denominator $ 1 > 0 $ â positive.

📌 For $ x > rac{11}{3} $, say $ x = 4 $: numerator $ -12 + 11 = -1 < 0 $, denominator $ 2 > 0 $ â negative.

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