Mathematics — first biennium · Lesson
In a rational equation, domain restrictions come before transformations: an algebraic solution must be rejected if it makes an original denominator zero.
Prerequisites: Algebraic-fraction operations and linear equations
Goal: State domain restrictions, clear denominators and verify that the solution is admissible.
In this lesson: State domain restrictions, clear denominators and verify that the solution is admissible.
New concept: In a rational equation, determine excluded values first. Then clear denominators using equivalent transformations on the allowed domain and finally check every obtained solution against the domain restrictions.
How to proceed: Find the forbidden value first. Then multiply both sides by the denominator and finally compare the solution with the domain restriction.
You can already assume: Algebraic-fraction operations and linear equations.
Completed exercises: 0/5 · Correct on first attempt: 0
Find the forbidden value first. Then multiply both sides by the denominator and finally compare the solution with the domain restriction.
Data / situation: Solve (x+9)/(x-3)=4.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.