Maths Extension 1 Year 11 - Module 1 - Lesson 3
Rational Inequalities
Name
Date
Class
1. Lesson focus
Rational inequalities and sign charts. Mark numerator zeros and denominator exclusions separately; test the signs on the intervals they create.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. Solve (x+3)/(x−1)≤0.
3. Solve (x−4)/(x−2)≥0.
3. Challenge
Solve (x−1)(x+2)/(x−3)<0.
4. Multiple choice
For (x+1)/(x−2), which value is excluded from the domain?
A. x=−1
B. x=2
C. x=0
D. none
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Solve (x−2)/(x+1)>0.
Critical values −1 (excluded) and 2 (zero); signs give x<−1 or x>2.
2. Solve (x+3)/(x−1)≤0.
Critical values −3 (zero) and 1 (excluded); the expression is non-positive on [−3,1).
3. Solve (x−4)/(x−2)≥0.
Critical values 2 (excluded) and 4 (zero); signs give x<2 or x≥4.
Challenge. Solve (x−1)(x+2)/(x−3)<0.
Critical values −2,1,3; sign chart gives (−∞,−2)∪(1,3), with roots/pole excluded.
Multiple choice. For (x+1)/(x−2), which value is excluded from the domain?
Correct answer: B. The denominator is zero at x=2, so that input is excluded regardless of the numerator.
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