SAT Math Practice Question #478 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #478

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

What is the sum of all valid solutions to the equation below? \[ \frac{x}{x - 3} - \frac{2}{x + 3} = \frac{18}{x^2 - 9} \]
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Identify the quadratic form: consider converting to vertex form \( y = a(x-h)^2 + k \) or using \( x = - rac{b}{2a} \) to find the line of symmetry.

Elimination Framework (Hint 2)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

This question tests your ability to solve rational equations AND your vigilance against the SAT's favorite trap: extraneous solutions. Step 1: Clear the denominators. Notice that the denominators are \( (x - 3) \), \( (x + 3) \), and \( x^2...

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

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