Generally, if A and B represent two integers and B contains letters, the formula

Second, the conditions related to the score

① The score is meaningful: the denominator is not 0(B? 0)

② The score is meaningless: the denominator is 0(B? 0)

③ The fractional value is 0: the numerator is 0 and the denominator is not 0 (? A is a fraction, a is a numerator and b is a denominator. b？ Answer? 0)

? b？ 0

? Answer? 0? Answer? 0 or? )B？ Is it? 0

? Answer? 0? Answer? 0 or? )

? b？ 0? b？ 0④ The fractional value is positive or greater than 0: numerator and denominator have the same sign (? ⑤ The fractional value is negative or less than 0: numerator and denominator symbol (?

⑥ The fractional value is 1: the numerator and denominator are equal (A=B).

⑦ The fractional value is-1: the numerator and denominator values are reciprocal (A+B=0).

Third, the basic nature of the score

The numerator and denominator of the (1) fraction are multiplied (or divided) by an algebraic expression that is not equal to 0, and the value of the fraction remains unchanged. Letters indicate: AA? CAA？ c？ ,? , where a, b and c are algebraic expressions, and c? 0。 BB？ CBB？ C

(2) Symbolic Law of Fraction: If you change any two of the numerator, denominator and symbol of the fraction itself, the value of the fraction remains unchanged, namely: a? Answer? AAB？ BB？ B

Note: when applying the basic properties of scores, we should pay attention to C? 0 this restriction and implied condition b? 0。

Fourth, the score of the score.

1. Definition: 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.

2. Step: Factorize the denominator of the fractional numerator, and then remove the common denominator of the numerator and denominator.

3. There are two cases: ① When the numerator and denominator of the score are single items, they can be simplified directly, and the greatest common divisor of the numerator and denominator coefficients can be simplified, and then simplified.

Remove the lowest power of the numerator and denominator.

(2) If the numerator denominator is a polynomial, factorize the numerator denominator first, and then divide it.

4. simplest fraction's definition: When the numerator and denominator of a fraction have no common factor, it is called simplest fraction.

About timesharing. Determination of common factor of numerator and denominator;

1) coefficient takes the greatest common divisor of the numerator and denominator coefficients as the coefficient of the common factor.

2) Take the lowest power of each common factor as the factor of the common factor.

3) If the numerator and denominator are polynomials, factorize the numerator and denominator first, and then judge the common factor.

V. General points of scores

1. Definition: It is called the general fraction of a fraction to change several fractions with different denominators into fractions with the same denominator equal to the original fraction.

(foundation: the basic nature of the score! )

2. The simplest common denominator: take the product of the highest power of all factors of each denominator as the common denominator, and such a common denominator is called the simplest common denominator.

How to determine the simplest common denominator in general division;

1. coefficient takes the least common multiple of each denominator coefficient as the coefficient of the simplest common denominator.

2. Take the highest power of each common factor as the factor of the simplest common denominator.

3. If the denominator is polynomial, it is necessary to factorize each denominator first, and then judge the simplest common denominator.

3. "Two types and three types"

The general classification of "two categories" means: first, the denominator is a single item; Second, the denominator is a polynomial.

"Three categories" under "two categories": "two or three categories", "two or four categories" and "four or six categories"

1) "two, three" type: it means that there is no relationship between several denominators, and the simplest common denominator is their product;

2) "two, four" type: refers to the denominator whose denominator completely contains another denominator, and the simplest common denominator is one of them;

3) "four, six" type: it means that several denominators have the same factors, but they also have unique factors. The simplest common denominator must have a unique factor.

It should also include the same factors.

4. General scoring method: first observe whether the denominator is single or polynomial. If it is a denominator monomial, then continue to consider what type it is, find out the simplest common denominator, and make a total score; If the denominator is a polynomial, first decompose the principal factor that the denominator can decompose, consider what type, and continue the division.

Six, the four operations of the fraction and the power of the fraction

1 fractional multiplication and division method: aca? cbdb？ d

Akada? D Fraction Divided by Fraction: After the numerator and denominator of division are reversed, multiply by divisor. The expression is:? bdbcb？ C Fraction is multiplied by fraction, the product of molecules is the numerator of the product, and the product of denominator is the denominator of the product. The formula is expressed as:

Ann? Answer? ② Power of Fractions: Power the numerator and denominator respectively. The formula is: nb? b？

③ Rules for addition and subtraction of scores:

1) Addition and subtraction of fractions with the same denominator: the denominator is unchanged, and the numerator is added and subtracted. The formula is: Na Ba? blind courtesy copy

acad？ Bcbdbd2) Addition and subtraction of fractions with different denominators: divide first, turn it into fractions with the same denominator, and then add and subtract. The formula is expressed as:

3) Two kinds: one is the addition and subtraction between scores; The second is the addition and subtraction of algebraic expressions and fractions (the denominator of algebraic expressions is 1).

Note: Algebraic expression and fractional addition and subtraction: Algebraic expression can be regarded as an integer, with a negative sign in front of it and brackets, as a fraction with denominator of 1, and then divided by it.

(4) The operation sequence of the mixed operation of addition, subtraction, multiplication, division and multiplication of fractions.

Power first, then multiply and divide, then add and subtract. In the operation at the same level, whoever counts first and counts first with brackets should also pay attention to flexibility to improve the quality of problem solving.

Note: In the process of operation, it is necessary to make clear the purpose and basis of each step of deformation, and pay attention to the standard format of problem solving, and do not skip steps casually so as to check correctly.

Whether there is an error or the cause of the analysis error.

The result of addition and subtraction must be reduced to the simplest fraction (or algebraic expression).

Seven. Integer exponential power

(1) After introducing negative integer and zero exponential power, the range of exponent is extended to all real numbers, and the law of positive integer power refers to negative integer.

The same applies to numbers and power. Namely:

Me? Ann? Me? National manufacturers association

nnn？ amn？ abanbnam？ Ann? Me? n(a？ 0) 1an？ an0na？ na？ 0)a？ 1(a？ 0) (the zeroth power of any number that is not equal to zero is equal to 1)ab? b？

Where m and n are integers.

Eight. fractional equation

1. Fractional equation: refers to an equation whose denominator has fractions and unknowns.

2. Steps to solve the fractional equation:

(1) Simplify first and then simplify.

(2) Remove the denominator and multiply both sides of the equation by the simplest common denominator of each denominator. (The process of generating additional roots)

(3) Solving the integral equation to obtain the solution of the integral equation.

(4) Testing, substituting the solution of the obtained integral equation into the simplest common denominator: if the simplest common denominator is 0, the original equation has no solution, and the value of this unknown is the root of the original equation; If the simplest common denominator is not 0, it is the solution of the original equation.

Note: The conditions for increasing roots are ① the solution of the obtained integral equation; (2) into the simplest common denominator, the value is 0.

9. Fractional equation-basic steps: review, design, column, solution, and answer (the solution to the application problem of the same linear inequality group)

(1) Review-Review the topic carefully and find out the equivalence relationship.

(2) Assumption-setting unknowns reasonably.

③ Column-list the equations (groups) according to the equivalence relation.

(4) solution-solve the equation (group). Attention test

5 Answer-Answer the question.