Mathematics — first biennium · Lesson
In rational inequalities the domain is part of the solution: a denominator zero is always excluded, even when it is an endpoint selected by the sign chart.
Prerequisites: Product/quotient signs and algebraic-fraction domain
Goal: Solve simple rational inequalities by distinguishing numerator zeros from excluded denominator values.
In this lesson: Solve simple rational inequalities by distinguishing numerator zeros from excluded denominator values.
New concept: In rational inequalities, a numerator zero may belong to the solution when equality is allowed; a denominator zero never belongs to the domain and is always excluded.
How to proceed: The numerator may be zero because ≤ includes equality; the denominator, however, may never be zero.
You can already assume: Product/quotient signs and algebraic-fraction domain.
Completed exercises: 0/5 · Correct on first attempt: 0
The numerator may be zero because ≤ includes equality; the denominator, however, may never be zero.
Data / situation: Solve (x-1)/(x-3)≤0.
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.