The basic idea of solving fractional equation is to transform fractional equation into integral equation

The basic idea of solving fractional equation is to transform fractional equation into integral equation

① De denominator
Multiply both sides of the equation by the simplest common denominator (the simplest common denominator: ① the coefficient takes the least common multiple, ② the letter appears takes the highest power, and ③ the factor appears takes the highest power) at the same time to transform the fractional equation into an integral equation. If you encounter opposite numbers, don't forget to change the sign
② According to the steps of solving integral equation
If there are brackets, remove the brackets, pay attention to the sign change, merge the similar items, and change the coefficient to 1 to get the value of the unknown;
③ Root test
It is necessary to check the root after finding the value of the unknowns, because in the process of transforming the fractional equation into the integral equation, the range of the unknowns is expanded, and the increasing root may occur
If the simplest common denominator is equal to 0, the root is the increasing root. Otherwise, the root is the root of the original fractional equation. If all the roots are increasing roots, the original equation has no solution
If the fraction itself is approximately divided, it should also be tested
When solving practical problems with fractional equation, we should not only check whether the solution meets the equation, but also check whether it meets the meaning of the problem
In general, when solving a fractional equation, the solution of the integral equation obtained after removing the denominator may make the denominator of the original equation zero. Therefore, the solution of the integral equation should be substituted into the simplest common denominator. If the value of the simplest common denominator is not zero, it is the solution of the equation
Attention
(1) Pay attention to the denominator, do not miss the integral term
(2) Increasing root is the root of integral equation after denominator is removed, but it is not the root of original fractional equation
(3) Increase the root so that the simplest common denominator equals 0
induce
The basic idea to solve the fractional equation is to transform the fractional equation into an integral equation. The specific method is to "remove the denominator", that is, to multiply the simplest common denominator on both sides of the equation. This is also the general idea and method to solve the fractional equation

How to find the equal relationship between quantities when solving practical problems with equations? Give examples

First, find out the data in the topic, and then do more according to the topic. For example, last month was 100, this month was 90 more than last month. This is just to pay attention to the three data of 100, last month, 90, and get 100 and 190