ACT Math Practice Question #2113 (Hard) | Test Citadel
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ACT Math Difficulty: Hard

Digital ACT Math Practice Question #2113

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

For all $x > 2$, which of the following is equivalent to $\frac{1}{x - 2} - \frac{2}{x + 3}$?
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Socratic AI Engine Step-by-Step Derivation
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Plug in $x = 3$: $\frac{1}{1} - \frac{2}{6} = 1 - \frac{1}{3} = \frac{2}{3}$. Test Choice A with $x = 3$: $\frac{-3+7}{(1)(6)} = \frac{4}{6} = \frac{2}{3}$. Perfect match!

Masterclass Solution & Distractor Trap Analysis

Find a common denominator: $\frac{1(x + 3) - 2(x - 2)}{(x - 2)(x + 3)} = \frac{x + 3 - 2x + 4}{(x - 2)(x + 3)} = \frac{-x + 7}{(x - 2)(x + 3)}$. Note that $-2(-2) = +4$....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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