Sign analysis — higher-degree and fractional inequalities

Inequalities of degree $\ge 3$ and fractional ones are solved with a systematic 4-step method: factorise, find the zeros of each factor, build the sign table, read off the result. The sign table is a tool of surprising power: once learnt, any rational inequality becomes manageable. This section presents the method and applies it to a complete series of examples, from third degree to fractions with a common denominator.

• The sign-table method
• Third-degree inequality
• Simple fractional inequality
• Factors always of the same sign
• Inequality with a quadratic factor
• Fractional inequality with a common denominator
• A complete inequality from start to finish