(Rational) Equation with unknown denominator Edit the concept of fractional equation in this paragraph.

Fractional equation is a kind of equation, and the (rational) equation with unknown number in denominator is called fractional equation. For example, 100/x=95/x+0.35. Supplement: This part of knowledge belongs to elementary mathematics knowledge, and is generally studied in senior two. Edit the solution of this fractional equation.

① Remove denominator

Both sides of the equation are multiplied by the simplest common denominator (the simplest common denominator: ① the coefficient is the least common multiple; (2) the letters that appear occupy the highest power; (3) the factors that appear take the highest power), and the fractional equation is turned into an integral equation; Don't forget to change the sign when you meet the opposite number.

(2) Solve the whole equation step by step.

Move the term, if there are brackets, remove the brackets, pay attention to the sign change, merge similar terms, change the coefficient into 1, and find the unknown value;

③ Root inspection

After finding the value of the unknown quantity, it is necessary to check the root, because in the process of transforming the fractional equation into the whole equation, the range of the unknown quantity is expanded and the root may be increased. When finding the root, substitute the root of the whole equation into the simplest common denominator, and if the simplest common denominator is equal to 0, add the root. Otherwise, this root is the root of the original fractional equation. If the root of the solution is an increasing root, the original equation has no solution. If the score itself is divided, it should also be brought in for inspection. When solving an application problem with a column fraction equation, it is necessary to check whether the solution satisfies the equation and whether the solution satisfies the meaning of the problem. Generally speaking, when solving fractional equations, the solution of the whole equation after removing the denominator may make the denominator in the original equation zero, so we should substitute the solution of the whole equation into the simplest common denominator. If the value of the simplest common denominator is not zero, it is the solution of the equation.

give rise to

The basic idea of solving the fractional equation is to turn the fractional equation into an integral equation, and the specific method is to "remove the denominator", that is, both sides of the equation are multiplied by the simplest common denominator, which is also the general idea and practice of solving the fractional equation. Example: (1) x/(x+1) = 2x/(3x+3)+1Multiply both sides by 3 (x+1) 3x = 2x+(3x+3) 3x = 5x+3-2x. X=-2/3 is the equation (2) 2/(x-1) = 4/(x 2-1) multiplied by (x+1) (x+65438+. So the original equation 2/x- 1 = 4/x 2- 1 has no solution and must be tested! Test format: bring x=a into the simplest common denominator. If x=a makes the simplest common denominator 0, then a is the root of the original equation. If x=a makes the simplest common denominator not zero, then a is the root of the original equation. Note: Whether there is a solution can be judged by experience. If there is a solution, calculate all denominators; If there is no solution, bring in the denominator without solution to edit the fractional equation application problem in this paragraph.

The general steps of solving application problems by time-sharing equation are: finding equivalence relation-setting-column-solution-answer-test. Example: The distance from Nanning to Kunming West Railway Station is 828 kilometers, and the ordinary train from Nanning to Kunming is faster than the through train. The speed of the through train is 1.5 times that of ordinary express. Two hours after the departure of ordinary express, the through train leaves four hours earlier than the ordinary train. Let's find the speed twice. If the speed of the ordinary train is x kilometers per hour and the through train is 1.5x, then the time of the ordinary train is 828/x hours, the through train is 828/65,438+0.5x, and the ordinary train starts two hours earlier and arrives four hours later. So the difference is 6 hours, so 828/x-828/1.5x = 6 (828 *1.5-828)/1.5x = 6414/1.5.