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).

When finding the root, substitute the root of the whole equation into the simplest common denominator. If the simplest common denominator is equal to 0, this root is an increasing root. Otherwise, this root is the root of the original fractional equation. If all the roots are augmented, the original equation has no solution.

Example: A road maintenance team has built a 300-meter-long road, and the actual daily maintenance distance is 10 meter longer than originally planned, which can be completed five days ahead of schedule. Q: How many meters of roads were originally planned to be built every day?

Suppose the original plan was to build roads x meters a day.

The original planned time is 300/X, and the actual time is 300/(x+5).

300/X-300/(X+ 10)=5

The first step in solving this fractional equation is to multiply both sides by the simplest common denominator X(X+ 10) to obtain

300(X+ 10)-300 X = 5X(X+ 10)

After it becomes an integral equation, it will be easy and simplified.

5X？ +50X-3000=0

x？ + 10X-600=0

(X+30)(X-20)=0

X=-30 or X=20.

After solving the unknown, it depends on whether it is realistic. For example, X=-30 is an unrealistic solution and should be deleted.

It was originally planned to build 20 meters of roads every day.

The above fractional equation does not produce an increase in roots. Here is another example to illustrate what root increase is and how to test it.

Solve the fractional equation: 2/(X-2)+6X/(X? -4)=3/(X+2)

The first step is to multiply by the simplest common denominator (X-2)(X+2).

2(X+2)+6X=3(X-2)

The second step is to solve the whole equation above.

8X+4=3X-6

5X=- 10，X=-2

Step 3, verify whether X=-2 is root growth.

Substitute X=-2 into (x-2) and (x+2).

(-2-2)(-2+2)=-4*0=0

X=-2 is an increasing root, so the original fractional equation has no solution.