The basic properties of the fractional equation in junior high school mathematics The numerator and denominator of the fractional equation are all multiplied by (or divided by) the same algebraic expression that is not equal to zero, and the value of the fractional equation remains unchanged.
That is, A/B=A+C/B+C(C≠0), where a, b and c are all algebraic expressions. The sign law of fraction: the numerator, denominator and sign of a fraction itself have changed, but the value of the fraction remains unchanged.
Conversion: scores can be converted, scores are similar to scores, and they can also be converted. According to the basic properties of a fraction, reducing the common factor of the numerator and denominator of a fraction is called the reduction of the fraction.
Fraction reduction step: (1) If the numerator and denominator of a fraction are in the form of a single item or the product of several factors, their common factors will be reduced; (2) The numerator and denominator of a fraction are polynomials, which are decomposed into factors respectively, and then the common factor is removed.
General fraction: According to the basic properties of fractions, the numerator and denominator are multiplied by an appropriate algebraic expression at the same time, and several fractions with different denominators are converted into fractions with the same denominator equal to the original fraction, which is called the general fraction of fractions. The general division steps of fractions: first find the simplest common denominator of all fractions, and then change the denominator of all fractions into the simplest common denominator; At the same time, each fraction expands its own numerator according to the multiple of denominator.
Typical mathematical exercises of fractional equation