; (2) According to the steps of solving the integral equation (shifting terms, merging similar terms and converting them into 1), the unknown value is obtained.
; ③ Root test (root test is needed after finding the value of the unknown quantity, because in the process of transforming the fractional equation into the whole equation, the range of the unknown quantity is expanded, which may lead to the increase of roots).
When finding the root, substitute the root of the whole equation into the simplest common denominator. If the simplest common denominator is equal to 0, this root is an added root. Otherwise, this root is the root of the original fractional equation. If the root of the solution is a Zeng root, the original equation has no solution.
If the score itself is about points, it should also be tested.
When solving an application problem with a column fraction equation, it is necessary to check whether the solution satisfies the equation and whether the solution satisfies the meaning of the problem.
factoring
1 Method of finding the common factor: Generally speaking, if every term of a polynomial has a common factor, you can put this common factor in parentheses and write the polynomial as a product of factors. This method of decomposing factors is called extracting common factors.
am+bm+cm=m(a+b+c)
Using formula method
① variance formula:. a 2-b 2 = (a+b) (a-b)
② Complete square formula: a 2 2ab+b 2 = (a b) 2.
③ Cubic sum formula: A 3+B 3 = (A+B) (A 2-AB+B 2).
Cubic difference formula: a 3-b 3 = (a-b) (a 2+ab+b 2).
④ Complete cubic formula: a 3 3a 2b+3ab 2 b 3 = (a b) 3.
⑤a^n-b^n=(a-b)[a^(n- 1)+a^(n-2)b+……+b^(n-2)a+b^(n- 1)]
A m+b m = (a+b) [a (m-1)-a (m-2) b+...-b (m-2) a+b (m-1)] (m is an odd number).
Component solution: a method of grouping polynomials and then decomposing factors.
4. Methods of splitting and supplementing projects
Decomposition and supplement method: one term of polynomial is decomposed or filled with two terms (or several terms) which are opposite to each other, so that the original formula is applicable to common factor method, formula method or group decomposition method; It should be noted that the deformation must be carried out under the principle of equality with the original polynomial.
Cross multiplication
① factorization of x2+(p q) x+pq formula.
The characteristics of this kind of quadratic trinomial formula are: the coefficient of quadratic term is1; Constant term is the product of two numbers; The coefficient of a linear term is the sum of two factors of a constant term. So we can directly decompose some quadratic trinomial factors with the coefficient of 1: x 2+(p q) x+PQ = (x+p) (x+q).
② Factorization of KX2+MX+N formula
If it can be decomposed into k = AC, n = BD and AD+BC = M, then
kx^2+mx+n=(ax b)(cx d)
a \ - /b ac=k bd=n
c / - \d ad+bc=m
take for example
Factorization x 2-x 2 = 0
Because x 2 = x times x
-2=-2 times 1
x -2
x 1
Diagonal multiplication and addition =x-2x=-x
Horizontal writing (x-2)(x+ 1)