Question

A 1. What is a rational inequality?​

Answer 1

Ответ:

Объяснение:I think this is what is needed.

Answer 2

A rational inequality is an inequality that involves one or more rational expressions. A rational expression is a fraction in which the numerator and denominator are both polynomials. In a rational inequality, you have one or more of these rational expressions and you're interested in determining the values of the variable(s) that satisfy the inequality.

Here's a general form of a rational inequality:

$\frac{P(x)}{Q(x)} \operatorname{<}, \operatorname{>} \operatorname{\leq}, \operatorname{\geq} 0$

Where:

• $P(x)$ and $Q(x)$ are polynomial expressions in $x$.
• The inequality symbol ($<$, $>$, $\leq$, or $\geq$) indicates the type of inequality being considered.
• The inequality is typically solved for values of $x$ that make the rational expression on the left side either positive (greater than zero) or negative (less than zero), depending on the context of the problem.

To solve a rational inequality, you often follow these steps:

1. Find the critical points: Determine the values of $x$ where the numerator ($P(x)$) and denominator ($Q(x)$) of the rational expression are equal to zero. These values are called critical points.

2. Create a sign chart: Use the critical points to divide the number line into intervals. In each interval, determine the sign (positive or negative) of the rational expression by testing a value from that interval.

3. Solve the inequality: Depending on the inequality symbol and the signs of the rational expression in each interval, you can determine the ranges of $x$ values that satisfy the inequality.

Rational inequalities often arise in various areas of mathematics, including algebra, calculus, and real-world applications, where relationships between quantities are expressed as fractions or ratios. Solving these inequalities allows you to understand the behavior of these relationships under different conditions.