Solution of fractional equation: ① denominator (both sides of the equation are multiplied by the simplest common denominator at the same time, and the fractional equation is transformed into an integral equation); (2) According to the steps of solving the integral equation (shifting terms, merging similar terms, and converting the coefficient 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). In the root test, the root of the whole equation is substituted into the simplest common denominator. If the simplest common denominator is equal to 0, this root is the root increase. 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 meets the equation and the factorization of the problem meaning 1. Common factor method: Generally, if each term of a polynomial has a common factor, you can put this common factor outside brackets and write the polynomial as a product of factors. This factorization method is called common factor method. AM+BM+CM = M (A+B+C) Use formula method ① Square difference formula:. A 2-B 2 = (A+B) (A-B) ② Complete square formula: A 2 2AB+B 2 = (A B) Cubic difference formula: a 3-b 3 = (a-b) (a 2+ab+b 2). ④ complete cubic formula: a33a2b+3ab2b3 = (a b) 35n-b n.am+b m = (a+b) [a (m-1)-a (m-2) b+...-b (m-2) a+b (m). 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 factorize some coefficients as1:x2+(p q) x+pq = (x+p) (x+q) 2kx2+MX+n If we can factorize it into K =, then kx2+MX+n = (AXB) (CX d) a \-/B ac.