SATAdvanced (700+)Frequency: 1 - 2 questions
Rational Equations & Extraneous Solutions
When solving rational equations by multiplying through by a common denominator, you may introduce extraneous solutions—solutions that make a denominator equal to zero in the original equation.
Core Formula & Concept Cheat Sheet
1Multiply all terms by the Lowest Common Denominator (LCD).
2Always check solutions back into the ORIGINAL denominators: Denominator ≠ 0.
3If a solution makes denominator 0, it MUST be discarded as extraneous.
The 700+ Score Trap
Counting an algebraic solution that makes the original denominator zero.
Test Your Mastery
Official Exam FormatLive Interactive Practice Drill
What is the solution set for the equation (x + 2) / (x - 3) = 5 / (x - 3)?
Frequently Asked Questions
How can I verify quickly with Desmos?
Graph the left side as y1 and right side as y2. Look for the intersection point. If a solution is extraneous, the graph will have a vertical asymptote or hole instead.