This is a formula, a fixed pattern. If not, it can't be solved. You can use the undetermined coefficient method to try (or prove).

1/[(x-a)^n(x-b)^m]=a 1/(x-a)^n+a2/(x-a)^(n- 1)+...+an/(x-a)

+b 1/(x-b)^n+b2/(x-b)^(n- 1)+...+bn/(x-b)

Extended data

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1. In China, students of science and engineering (except mathematics, students majoring in mathematical analysis) have difficulty in learning mathematics, which is often called "advanced mathematics" in textbooks; Students majoring in literature and history learn mathematics a little shallower, and their textbooks are often called "calculus".

2. Different majors in science and engineering, literature and history have different degrees of depth. It is advanced mathematics that studies variables, but advanced mathematics does not only study variables. As for the courses related to "advanced mathematics", there are usually: linear algebra (advanced algebra for mathematics majors), probability theory and mathematical statistics (some mathematics majors study independently).

3. Elementary mathematics studies constants and uniform variables, and advanced mathematics studies non-uniform variables. Advanced mathematics (the general name of several courses) is an important basic subject in science and engineering colleges, and it is also a compulsory mathematics course for non-mathematics majors in science and engineering, as well as a compulsory course for other majors.

4. As a basic science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstraction and computability are the most basic and remarkable characteristics of mathematics. With a high degree of abstraction and unity, we can profoundly reveal its essential laws and make it more widely used.

5. Strict logicality means that in the induction and arrangement of mathematical theories, whether it is concepts and expressions, or judgments and reasoning, we must use the rules of logic and follow the laws of thinking. Therefore, mathematics is also a way of thinking, and the process of learning mathematics is the process of thinking training. The progress of human society is inseparable from the wide application of mathematics.

6. Especially in modern times, the appearance and popularization of electronic computers have broadened the application field of mathematics. Modern mathematics is becoming a powerful driving force for the development of science and technology, and it has also penetrated into social sciences extensively and deeply.

References:

Baidu encyclopedia-advanced mathematics