Junior high school math problems fractional equations, how to solve fractional equations in junior h

1) (x-3 x-2)+1=3 (2-x) solution: (x-3) (x-2)+1=-3 (x-2) The two sides of the equation are multiplied by x-2 to obtain :

x-3+x-2=-3

2x-5=-3

2x=2 x=1

Check: When x=1, x-2≠0

x=1 is the solution of the original fractional equation.

2) x (x-3) = (x+1) (x-1) solution: multiplication of both sides of the equation (x-3) (x-1) yields:

x(x-1)=(x+1)(x-3)

x²-x=x²-2x-3

x=-3 test: When x=-3, (x-3)(x-1) ≠0x=-3 is the solution of the original fractional equation.

1) Solution: (x-3) (x-2)+1=3 (2-x)x-3) (x-2)+1=-3 (x-2) multiply x-2

x-3+x-2=-3

2x=2 x=1

After testing, x=1 is the solution of the equation.

2) Solution: x-1 x-3=x+1 x-1

x-1)²=(x+1)(x-3)

x²-2x+1=x²-2x-3

So x has no solution.

If you don't understand, you can ask and be satisfied) Thank you! Good luck with your studies!

In the first question, a negative sign is (x-3 x-2)+1=-3 (x-2), and the two-side multiplication (x-2) is (x-3)+(x-2)=-3, and then x-5=-3, x=1, test, the second question, multiply (x-1) (x-3), and get x(x-1)=(x+1)(x-3), and then get x 2-x=x 2-2x-3, and the solution is x=-3, and you have checked!

Steps to solve fractional equations in junior high school:1The denominator of the fractional equation can be factored first.

2.Find the simplest common denominator of each denominator in a fractional equation. 3.

The terms on both sides of the fractional equation are multiplied by the simplest common denominator at the same time to achieve the purpose of removing the denominator, and the equation has been reduced to an integral equation. 4.Solve this integer equation.

5.Inspection, if there is an increase in roots, it should be removed.

It can only be said to be a half-pair, first of all, in the process of "multiply both sides by (x-3), get x-3=-2(x-3)" This error may be that you made a mistake (you should get x a=-2 (x-3)).

And then you have to say it at the end because of X-3≠0

So x≠3, so (a+6) 3≠3

Therefore, a≠3 so the value range of a is a -6, and a ≠ 3

No, make sure that the numerator is not 0, i.e. x≠3

That is, (a+6) 3≠3 gives a≠3

In summary, a -6 and a ≠3

1.Assuming that the original plan is to repair x meters per day, then the equation is solved to get x=80

2.Let A process x pieces per day and B process y pieces per day, then 1200 x-10 = 1200 y, y =, solve the equation to obtain x=40, y=60;

3.Let A spread x kilometers per week and B spread y kilometers per week, then x+1=y, 18 x-3=18 y solve the equation to get x=2, y=3

Fractional equation solution:

Go to the 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. If you encounter numbers that are opposite to each other. Don't forget to change the symbols.

Lowest common denominator: The coefficient is the lowest common multiple, the unknown is the highest power, and the factor that appears is the highest power).

If there are parentheses, the parentheses should be removed first, pay attention to the variable signs, merge similar items, and turn the coefficient to 1 to find the value of the unknown;

After finding the value of the unknown, the root must be checked, because in the process of converting the fractional equation into an integral equation, the range of values of the unknown is expanded, and the root increment may be generated.

If the simplest common denominator is equal to 0, the root is an incremental root. Otherwise this root is the root of the original fractional equation. If the solved roots are all incremental roots, then there is no solution to the original equation.

If the fraction itself is divided, it should also be substituted for inspection.

When solving a problem with a column fractional equation, it is necessary to check not only whether the solution satisfies the equation, but also whether it conforms to 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 in the original equation zero, so the solution of the integral equation should be substituted into the simplest common denominator, and if the value of the simplest common denominator is not zero, it is the solution of the equation.

To solve the fractional equation, we should pay attention to the format, first remove the denominator, convert the fractional equation into a one-dimensional equation, then calculate and finally test.

Set the normal trace key, highway speed, attitude, and block x

600/x=2*480/(x+45)

600x+600*45=960x

360x=600*45

x=75600 plus 75=8 hours.

x 2=x+1, directly substituted, x 5=x 2*x 2*x=(x+1)(x+1)x=(x 2+2x+1)x=(3x+2)x=5x+3,x 4+2x+1=(x+1) 2+2x+1=5x+3, the final result is 1

(1) The ** of the souvenir in April is X yuan, which is derived from the title (2000 x + 20).

Solution x=50

2) Set the cost of each souvenir to be y yuan, from the title (2000-800) y = 2000 50

The solution is y=30

Yuan (where (2) x stands for multiplication sign) is so good to write that you must give points.

I don't know, just ask the junior high school students.