1. Transformational thinking is an important mathematical thinking method. The so-called transformation thinking is to transform the problem to be solved into another problem that is easy to solve or has been solved. Specifically, it is to transform "new knowledge" into "old knowledge", "unknown" into "known" and "complex" into "simple". Solving fractional equations often transforms fractional equations into integral equations to solve them.

2. Modeling idea: solving practical problems with mathematical knowledge. First of all, through observation and analysis, practical problems are transformed into mathematical problems. When solving practical problems with fractional equations, we should first find out the equivalence relation from practical problems, that is, establish a mathematical model, and then list fractional equations according to the mathematical model, so as to achieve the purpose of solving practical problems.

3. The idea of classified discussion: Specifically, the problem containing many possible situations is divided into several categories according to certain standards, and then each category is solved separately, so as to achieve the steps of solving the whole problem. The general principle of classification is: unified standards, no duplication.

4. Equation idea: By establishing unknown equations (groups), the problem to be solved can be solved or more easily.

5. The idea of combining numbers with shapes is to organically combine the relationship between figures and quantities, so that mathematical problems are more intuitive and easier to solve.

6. Thinking from the general to the special: first explore the parallelogram, then explore the special parallelograms such as rectangles, diamonds and squares, first explore the general and then explore the special, and look for features in the nature of * * *, which is the main method to explore knowledge.