Solving fractional problems in junior high school math, general steps in solving fractional equation

1 (a-b) = 1 b-1 a, multiply both sides by ab(a-b) at the same time to get ab=a(a-b)-b(a-b)After simplification, a 2 + b 2 = 3ab

a b+b a=(a 2+b 2) ab=3ab ab=3Note: 2 means squared.

1／a-b=1／b-1／a ==> 1/(a-b)=(a-b)/ab

(a-b)^2=ab ==> a^2+b^2=3ab

Then: a b+b a ==> (a 2+b 2) ab ==> Bring the above equation into : 3ab ab=3

1/(a-b)=(1/b)/(1/a)--1/(a-b)=(a-b)/ab---a2+b2=3ab---

a b) (b a) = (a2+b2) ab--- obtained from a2+b2=3ab: (a2+b2) ab=3

i.e. (a b) (b a) = 3

Note: is the square of a. b squared.

The results are out, so I won't write about it.

1) Steps to solve the fractional equation: remove the denominator; find the solution of the integer equation; Inspection; Draw conclusions

2) When solving the fractional equation, the solution of the integer equation obtained after removing the denominator may make the denominator in the original equation 0, so it should be tested as follows:

If the value of the simplest common denominator is not 0, then the solution of the integer equation is the solution of the original fractional equation

If the value of the simplest common denominator is 0, then the solution of the integer equation is not the solution of the original fractional equation

Therefore, when solving fractional equations, it must be checked

The two sides of the equation are multiplied by the lowest common denominator, and the fractional equation is reduced to an integer equation.

Solution: 2x=3-

2×｛2（x-1）｝

Go to the denominator. Multiply by 2 (x+1))2x=

3-4x+26x=555x

Check: Substitute x into 2 (x+1) ≠ 0

665 so.

x=——— is the root of the primitive fraction.

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I'm going to eat. I'll help you figure it out later)6

A fractional equation is a type of equation in which the denominator contains unknowns (rational) is called a fractional equation.

How to solve fractional equations.

Go to the denominator. The simplest common denominator is multiplied on both sides of the equation (the simplest common denominator: the coefficient is taken as the least common multiple, the letter that appears takes the highest power, and the factor that appears takes the highest power), and the fractional equation is reduced to an integral equation. If you encounter numbers that are opposite to each other. Don't forget to change the symbols.

Follow the steps to solve the integer equation.

Move items, if there are parentheses, remove the parentheses, pay attention to the change signs, merge similar terms, and turn the coefficient to 1 to find the value of the unknown;

After finding the value of the unknown, it is necessary to check the root, 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 addition 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 root is an additional root, then there is no solution to the original equation.

Example: (1)x (x+1)=2x (3x+3)+1 Multiply 3(x+1) 3x=2x+(3x+3) 3x=5x+3 -2x=3 x=2 -3 Fractional equation to be tested After testing, x=-2 3 is the solution of the equation.

2)2 (x-1)=4 (x 2-1) Multiplication (x+1)(x-1) 2(x+1)=4 2x+2=4 2x=2 x=1 Fractional equation to be tested Bring x=1 into the original equation so that the denominator is 0, which is the root increase. So the original equation 2 x-1=4 x 2-1 has no solution must be tested! Example:

2x-3+1 (x-5)=x+2+1 (x-5) subtract 1 (x-5) on both sides at the same time, and get x=5 Bring in the original equation so that the denominator is 0, so the equation has no solution! 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.

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First put the 2 of 2x-2, and then divide each co-multiplication x-1 about two fractions to solve it.

Commutation method. Let (2x 2-1) x=y

then the original equation is transformed into y+1 y=2

y²-2y+1=0

y-1）²=0

y=1So: (2x 2-1) x=1

2x^2-1)=x

2x^2-x-1=0

2x+1）（x-1）=0

x1=—，x2=1

It has been tested that x1=, x2=1 are the roots of the original equation.

Let's assume that the number of yearlings randomly inspected by the quality inspection department of the finch brigade is x (the same as A and B), then the equation can be listed:

a) 48 x - 45 x = 5%.

3/x=5%

x = 60 2) The pass rate of factory A products = 48 x * 100%, your Fang Min and Wang Cheng are listed wrong.

Number of days originally required: 240 a

Now 240 = 20 a

So the answer is 240 a - 20 a = 220 a hours.

It was originally planned to take 240 years

The actual time taken is 240 (

240 a-200 a=20 a