SAT Math Practice Question #240 (Hard (665)) | Test Citadel
TC
Test Citadel
SAT Math Difficulty: Hard (665)

Digital SAT Math Practice Question #240

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

Consider the rational equation below: \[ \frac{x^2 + 5x + 6}{x + 3} = x^2 + 2x - 4 \] What is the sum of all valid solutions \( x \) to the given equation?
Select Your Answer:
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 problem tests your ability to solve rational equations and, crucially, to check for extraneous solutions. Let's simplify the left side of the equation first. The numerator is a quadratic: \( x^2 + 5x + 6 \). We can factor this by findi...

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

🔒 Citadel Pro Scholar Vault

Unlock Full Solution & 2,600+ Official Drills

Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.

Socratic Assistant

Targeted hints without disclosing final solutions.

I am your Socratic tutor. Click one of the quick guidance buttons above or ask a specific question below about a formula or method.