Understanding Disequazioni Fratte (Fractional Inequalities)

This page provides a detailed explanation of disequazioni fratte, or fractional inequalities, along with disequazioni fratte esercizi svolti (solved exercises) to illustrate the concept.

The page begins by presenting the general form of a fractional inequality:

N(x) / D(x) > 0

Where N(x) represents the numerator and D(x) the denominator.

Definition: A disequazione fratta is an inequality where the variable appears in both the numerator and denominator of a fraction.

The solving process involves two main steps:

1. Setting the numerator equal to zero: N(x) = 0
2. Ensuring the denominator is greater than zero: D(x) > 0

Example: The page provides a specific example of a fractional inequality: (4 - x) / (x + 7) > 0

For this example:

• Numerator (N): 4 - x > 0
• Denominator (D): x + 7 > 0

The page then presents another example: (4x - 12) / (15 - 4x) > 0

For this more complex example:

• N: 4x - 12 > 0
• D: 15 - 4x > 0

Highlight: The page emphasizes an important rule: If the inequality sign in the original equation is ≥ or >, the variable x is considered in the "plus" region. If the sign is ≤ or <, x is considered in the "minus" region.

The page concludes with the solution to the second example: x < 3 or x > 4

Vocabulary:

• Numeratore: Numerator
• Denominatore: Denominator

This comprehensive guide provides a clear disequazioni fratte schema (scheme) for solving fractional inequalities, making it an excellent resource for students studying disequazioni fratte di primo grado (first-degree fractional inequalities) and disequazioni fratte di secondo grado (second-degree fractional inequalities).