How to solve fractional inequalities, how to solve fractional inequalities

Fractional inequalities are reduced to integer inequalities and solved. The solution of a fractional inequality is as follows: the first step is to remove the denominator, the second step is to remove the parentheses, the third step is to move the terms, the fourth step is to merge the same terms, and the fifth step is to reduce the coefficient of the unknown to 1.

If the right side of the fractional inequality is 0, the transformation method on the left side of the inequality can no longer be simplified: on the premise that the denominator is not 0, both sides are multiplied by the square of the denominator.

If the right side of the fractional inequality is not 0 or the left side of the inequality is not 0, the steps that can be simplified to convert to an integral inequality:

1. Shift the right side of the inequality to 0.

2. Divide the left side of the inequality.

3. The dichotomy inequality evolves into an integer inequality.

4. Turn the coefficients before the unknown x of the inequality into positive numbers.

1) Solve first (1-x) x>0

Because the numerator divides by the denominator greater than 0

Indicate that the numerator and denominator are the same.

The above equation is equivalent to: x(1-x)>0

i.e.: x(x-1)<0

Solution: 00Solution: x<0 or x>1 11

Moreover. x>-1

1 11 you contrast 1) and 2).

I think I'll be able to figure it out for myself.

It is to first sort out the molecular inequalities.

Reuse of original inequalities》0

or <0) is equivalent to the same (or different sign) of the numerator and denominator, and converts the fractional inequality into an integer inequality.

Solve again.

The left side of the inequality is simplified by (x-5 2) (x-3)(x-4) 0x-5 2 0,(x-3)(x-4) 0 or x-5 2 0,(x-3)(x-4) 0 by 3 x 4

By x 5 2

The solution of the original inequality is 3 x 4 or x 5 2

The steps of solving the fractional equation are the same, and at the end of the process, it is necessary to pay attention to the negative sign to change the sign and test.

That's it, we're going to exclude impossible numbers.

Multiply x-3 on both sides of this question

3x-1≥0

Solution x 1 3

Because x-3≠0

So x≠3

We get that the solution set is x 1 3 and x ≠ 3

To solve inequality 2 x-1>x requires the inequality to be simplified first.

According to the inequality 2 x-1>x, the inequality can be multiplied by x, and the inequality 2-x> x 2 can be obtained

Move 2-x to the right, and the inequality becomes x 2+x-2 0

According to the factorization, we can get the formula (x+2)(x-1) is x 2+x-2, and we can get (x+2)(x-1) 0

The solution is x -2 or x 1, and the optimal solution is x -2.

1. If x>0, both sides of the inequality are multiplied by x to obtain: x 2+x-2<0, and the solution of the inequality is -20, so in this case.

The solution is 00, and the inequality is solved by x>1 or x<-2, and since x<0 is assumed, the solution in this case is x<-2.

In summary, the solution of 2 x-1>x is 0< x<1 or x<-2< p>

Multiply x on both sides at the same time, and there are two cases: x>0, 2-x> x 2, x 2+x-2<0, (x+2)(x-1)<0, -20, x>1 or x<-2, x<-2

Overall: 0

The shilling denominator is not equal to zero, and then the main idea is to turn the fractional inequality into an integer inequality. When you see the integer and the fraction together, you must first pass the part, move 1 to the left of the inequality, (x-1) (2x+1)-(2x+1) (2x+1).

The solution to the fractional inequality is as follows:

You can use the principle of same solution to denominator and solve fractional inequality; e.g. f(x) g(x)>0 or f(x) g(x)<0;(where f(x) and g(x) are integers and g(x) is not 0), then f(x)g(x) > 0, or f(x)g(x) < 0. Then factor the change point and use the thread-and-needle method.

The first solution of fractional inequality is:

Let the numerator and denominator be equal to 0, and find the solution; Draw the number line to find the position of the solution on the number line; Determine the positive or negative of the product of the highest order coefficient of the numerator and denominator; If the product is positive, it crosses from the top right to the bottom; If it is negative, it will pass from the bottom right to the top.

The second solution to fractional inequality is:

Shifting terms and dividing the right side into 0, and the left side is in the form of fractions; Let the numerator and denominator be equal to 0, and find the solution; Draw the number line to find the position of the solution on the number line; Determine the positive or negative of the product of the highest order coefficient of the numerator and denominator; If the product is positive, it crosses from the top right to the bottom; If it is negative, it will pass from the bottom right to the top.

Considerations for solving inequalities.

1. Symbol: Multiply or divide a negative number on both sides of the inequality, and change the direction of the inequality sign.

2. Determine the solution set: if it is larger than both values, it is larger than the larger one; Smaller than both values, smaller than the smaller; Bigger than the big, smaller than the small, there is no solution; Bigger than the small, smaller than the big, there is a solution in the middle. A group of inequalities consisting of three or more inequalities, and so on.

Solution of fractional inequality:

Shift, the other side is zero, and then it is divided into shapes such as f(x) g(x) 0(0), and then equivalent to f(x)g(x) 0

The solution of the integer inequality.

Good luck!

The solution method of fractional inequality is: the denominator can be used to solve the fractional inequality by using the principle of same solution; If f(x) g(x)>0 or f(x) g(x)<0 (where f(x) and g(x) are integers and g(x) is not 0), then f(x)g(x)>0, or f(x)g(x)<0. Then factor the change point and use the thread-and-needle method.

Fractional inequalities are similar to fractional equations, like f(x) g(x)>0 or f(x) g(x)<0 (where f(x), g(x) are integers and g(x) is not 0), and inequalities with unknowns in the denominator are called fractional inequalities.

The first solution of fractional inequality is: let the numerator and denominator be equal to 0, and find the solution; Draw the number line to find the position of the solution on the number line; Determine the positive or negative of the product of the highest order coefficient of the numerator and denominator; If the product is positive, it crosses from the top right to the bottom; If it is negative, it will pass from the bottom right to the top.

The second solution of fractional inequality is as follows: shift the right side to 0, and the left side is in the form of a fraction; Let the numerator and denominator be equal to 0, and find the solution; Draw the number axis to find the position of the solution on the thick axis of several rulers; Determine the positive or negative of the product of the highest order coefficient of the numerator and denominator; If the product is preceding the code, it passes through from the top right down in turn; If it is negative, it will be passed from the bottom right to the top to get the calculation result.

Fractional inequalities are similar to fractional equations, such as f(x) g(x)>0 or f(x) g(x)<0 (where f(x), g(x) are integers and g(x) is not 0).Inequalities with unknowns are called fractional inequality.

Ordinary method – the core idea.

For example, in the three-bond family fractional inequality diagram, the fractional inequality is converted into an integer inequality, and then the method of integer inequality is used to solve it.

Simple solution. You can use the principle of same solution to denominator and solve fractional inequality;

For example, f(x) g(x) > manuscript cheats 0 or f(x) g(x)<0 (where f(x) and g(x) are integers and g(x) is not 0).

then f(x)g(x)>0, or f(x)g(x)<0.

Then factor the change point and use the thread-and-needle method.