Definition of Fractional Equation The definition made by Mathematics (Grade 8) of East China Normal University Edition: The equation contains fractions and the denominator contains unknowns. Equations like this are called fractional equations.

Definition of Fractional Equation The definition made by Mathematics (Grade 8) of East China Normal University Edition: The equation contains fractions and the denominator contains unknowns. Equations like this are called fractional equations.

Problem solving step editing

denominator

Multiply both sides of the equation by the simplest common denominator at the same time, and turn the fractional equation into an integral equation; If you encounter the opposite number. Don't forget to change the symbol.

(The simplest common denominator: ① coefficient takes the least common multiple ② unknown takes the highest power ③ the factor that appears takes the highest power)

Interchange of terms

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

Root test

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, which may increase the root.

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 added root. Otherwise, this root is the root of the original fractional equation. If all the roots are augmented, the original equation has no solution.

If the score itself is divided, it should also be substituted into the test.

When solving an application problem with a column fraction equation, it is necessary to check whether the obtained solution meets the equation and 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.

pay attention to

(1) Be careful not to omit the algebraic expression item when removing the denominator.

(2)_ root is the root of the integral equation formed after naming the fractional equation, but it is not the root of the original fractional equation.

(3)_ Root makes the simplest common denominator equal to 0.

(4) In the fractional equation, if X is the denominator, then X should not be equal to 0.