I. Definition of Fractional Equation
Fractional equation is a kind of equation, which refers to a rational equation with unknown or unknown algebraic expression in the denominator. This part of knowledge belongs to elementary mathematics knowledge.
Second, the main points of fractional equation
1. Important characteristics of fractional order equations: fractional order equations are equality; The equation contains a denominator; There are unknowns in the denominator.
2. The difference between fractional equation and integral equation lies in whether there are unknowns (not ordinary letter coefficients) in the denominator. An equation with unknowns in the denominator is a fractional equation, and an equation without unknowns in the denominator is an integral equation.
3. Relationship between fractional equation and integral equation: Fractional equation can be transformed into integral equation.
Third, the solution of fractional equation
The basic idea of solving fractional equation is to transform fractional equation into integral equation. The method of transformation is to multiply both sides of the equation by the simplest common denominator and remove the denominator. When the denominator is deformed, sometimes the root that makes the simplest common denominator zero may be generated, which is called the root increase of the original equation. Because increasing roots may occur when solving fractional equations, it is necessary to check the roots when solving fractional equations.
Fourth, the knowledge points of fractional equation
1, the basic property of the fraction: the numerator and denominator of the fraction multiply (or divide) the same algebraic expression that is not equal to 0, and the value of the fraction remains unchanged.
2. Whole root: The simplest root with a common denominator of 0 is called the whole root of fractional equation. The method of testing the solution of the fractional equation: substitute the solution of the integral equation into the simplest common denominator, and if the value of the simplest common denominator is not 0, the solution of the original fractional equation is explained; Otherwise, this solution is not the solution of the original fractional equation.