SAT Math Practice Question #267 (Hard (725)) | Test Citadel
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SAT Math Difficulty: Hard (725)

Digital SAT Math Practice Question #267

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What is the sum of all valid solutions to the given equation? \[ \frac{x^2 - 3x}{x + 2} = \frac{10}{x + 2} + 2 \]
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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

Get ready, because this question contains one of the most lethal traps on the entire SAT Math section: the extraneous solution! Let's solve it safely together. Step 1: Clear the denominators. The easiest way to solve a rational equation is ...

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

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