Rational Inequalities (Leaving Cert Mathematics): Flashcards

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Rational Inequalities
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Form of rational inequality

ax+bcx+d\frac{ax+b}{cx+d} (ratio of two linear functions)

Issue multiplying by (x+2)(x+2) in rational inequality

Don't know if it's positive or negative

Why (x+2)(x+2) sign matters in rational inequalities

Determines whether to switch inequality sign

Method to avoid sign issue in rational inequalities

Multiply both sides by (x+2)2(x+2)^2

Why squared expressions solve the sign problem

Any expression squared is guaranteed to be positive

Effect of multiplying by positive on inequality sign

Don't have to switch the inequality sign

Step after multiplying by (x+2)2(x+2)^2 in example

Cancel common factor of (x+2)(x+2)

Method to find roots of resulting quadratic

Quadratic formula

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Inequalities

Modulus

Inequality Proofs & Discriminants

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Inequalities

Modulus

Inequality Proofs & Discriminants

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Inequalities

Modulus

Inequality Proofs & Discriminants

Explore Leaving Cert Mathematics Exam Questions by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

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