1, identify the form of the equation and denominator: it is necessary to identify the form of the equation, which is helpful to determine the best method to solve the equation. In a fractional equation, the denominator can be a polynomial or a more complex expression. In order to make the equation easier to solve, we need to find a way to simplify the denominator into a more manageable expression. This is usually achieved by "multiplying by the least common multiple".
2. Move the term, merge similar terms and simplify the equation: move the term in the equation to one side of the equation to make it easier to solve the equation. This is usually achieved by "moving the project". Similar terms in the equation are merged together to solve the equation more easily. This is usually achieved by "merging similar projects". By removing denominator, moving terms and merging similar terms, the equation becomes simpler.
3. Solve the equation and verify the solution: use appropriate mathematical methods (such as algebra and factorization). ) to solve the equation. After finding the solutions of the equations, it is necessary to verify whether these solutions are correct. This is usually achieved by substituting the solution into the original equation. If the left and right sides of the original equation are equal, the solution is correct; Otherwise, it is necessary to reconsider the derivation process of the solution and solve it again.
The Origin of Fractional Equation
1. Background: The appearance of fractional equation is closely related to the solution of practical problems. In real life, we often encounter some problems that need to be described by mathematical models, such as the relationship between speed, time and distance, or the mixture of solutions. The mathematical models of these problems usually involve fractional equations.
2. Application: Fractional equation is widely used in various fields. For example, in physics, fractional equations can be used to describe the relationship between acceleration and velocity in mechanics; In chemistry, fractional equation can be used to describe the relationship between chemical reaction rate and reactant concentration; In economics, fractional equation can be used to describe the relationship between investment return and interest rate.
3. Development: With the development of mathematics, the theory and solution method of fractional equation are constantly improved. For example, joseph liouville, a mathematician in the19th century, put forward the Liouville theorem, which provided theoretical support for solving fractional equations. At the same time, many mathematicians have developed various methods to solve fractional equations, such as gauss elimination and iterative method.