The problem of calculating the first two scores

1, when the score is meaningful; When is, the decimal value is zero.

2、 ; If yes, the value range of x is;

3. Without changing the numerical value of the formula, convert the numerator and denominator of the fraction into integers.

4. If the value of the score is a positive integer, then the integer x =；; The value of x that makes the score meaningless is.

5. The simplest common denominator of fractions and sums is.

6. Among these scores, the simplest one is.

7. If the value of the score is 10, the value of the score will be.

8, known, then =;

9. Observe the numerical characteristics of the following equations:,,, .............................................................................................................................................................

10, known as a real number, and, if, the size relationship is.

Second, choose:

1. In the algebraic expression,,,,, the number of fractions is ().

a， 1 b，2 c，3 d，4

2. The range of X that makes the formula meaningful is (). a、x > 0 b、x≠ 1 C、x ≠- 1 d、x≠ 1。

3. The simplest common denominator of fractional sum is ().

(A) (B) (C) (D)

4, the following calculation is correct ()

A.； BC; D.

5. Among the following scores, the simplest one is () A.B.C.D 。

6. If 3x=2y, the value of is equal to () a, b, 1 C, d,

7. The correct result of simplification is () a, 0 B, c, 1 D, and none of the above conclusions are correct.

8. The condition for making the score positive is () a, x.

9. Given that X is an integer and the value of the fraction is an integer, the acceptable value of X is () a.1b.2c.3d.4.

10, observe the following equation:

; ; ; …; Add the above equation and you get it. Calculated by the above method, the result is ()

A.B. C. D。

Third, answer questions:

1, calculation: (1) (2)

(3) (4)

(5) (6)

(7)x+y- (8)a-2b+

(9)

(10) Simplify first, and then replace the evaluation with your favorite number:

(1 1) Solve the equation:.

2. It is known to find the following values: (1); (2) .

3. Simplify first, then choose a suitable value that you like best and substitute it in the evaluation.

4, known, find the value of the score;

5. Known and valuable;

Step 6 calculate

And find the value of the algebraic expression when x= 1

7. If the given score is greater than 2, find the range of X;

8. It is known that X is an integer, and it is an integer. Find the sum of all qualified x values.

9. Let's look at the specific process of a classmate solving the following fractional equation.

solve an equation

. ①

. ②

. ③

∴x -6x+8= x -4vx +3，④

∴x=。 ⑤

X= is the solution of the original equation.

Please answer: (1) The specific way to obtain ② is; ② The specific ways to obtain ③ are:

The reason for getting ④ is.

(2) Is the above solution correct? If not, please point out the cause of the error and correct it on the right.

10. Does the fractional equation have a solution when k takes a combined value?

1 1. If the solution of the equation is positive, find the range of a. 。

12. Known trial values

Practice of adding and subtracting scores;

1. Given two fractions A= B=+, the following statement is correct.

A, A=B B, a and b are the reciprocal of c, a and b are the opposite numbers of d, so it is impossible to determine.

2. If x>y>0, then _

A.0 B. positive number C. negative number D. integer

3.a+b- equals A.-B.-C.D.-

4. Given X = 1- and Y = 1-, the algebraic expression of X and Z should be

A.B. C. D。

5. If x+y =-5 and xy = 3, the value of+is a.-b.-c.1d. 。

( 1) (2)

2x + -4y (4)

7. Known

(1) Find the values of A and B (2) Use the solving process of (1) to change the score into the sum of two scores.

(3) Use the above method to calculate the following two questions.

① ②

Supplementary exercises of fractional multiplication and division

The arithmetic multiplication rule of fractions: Fractions multiplied by fractions; that is

Law of fractional division: Fraction divided by Fraction; That is to say,

For fractions whose numerator or denominator is polynomial, polynomial should be performed first, and the calculation result should be changed to

The mixed operation of multiplication and division of fractions can be unified as: then

In the mixed operation, the power is calculated first, and the multiplication and division belong to the same level of operation, such as a2÷ b. =

Calculation: (1) (2)

(3) Simplify the fraction first, and then choose a number from 1,-1, 0,2,2 to find its value.

(4) Simplify first, then evaluate: (5) Know k and find its value.

Where a is the root of the equation x2+3x+ 1=0.

(6) It is known that the solution of the equation about x is x=2, where A ≠ 0 and B ≠ 0, and the value of the algebraic expression is found.

(7) Suppose a+b+c=0, please explain:

1, the length of the trapezoid midline is m and the area is s, then its height is;

2. In the score, when y=, the score is meaningless; When y=, the fractional value is 0;

3. When x=, the value of the score is 0;

4. A factory originally planned to complete B products in one day, but if it needs to be completed X days in advance now, it will produce _ _ _ _ _ _ more products every day than before;

5, in the score, when x is, the score is meaningful; When x=, the fractional value is 0.

Second, choose:

1, among the following, belongs to the fraction is ().

A.2+ B. C. D. (a+b)

2. If the score is meaningful, then ()

A.x ≠ 2b.x ≦-1c.x ≦-1and x ≠ 2d.x >; 2

3. No matter what value X takes, the following score is always meaningful ().

A. B.C.

4. When x =-, the following score is meaningful ().

A.B. C. D。

5. If the value of the score is 1, the value of x is ().

a . x≥0 b . x & gt； 3 C.x≥0 and x≠3 D. x≠3

Third, answer questions:

1. What number does the following score mean when x is taken?

①.②.③.

2. when x=2, the time division formula is meaningless, so find a.

3. Find the value of the following score:

①, where x =-②, where x =- 1, y =-

) When taking the value of m, does the equation 5/(x-2) = m/(x 2-4)+3/(x+2) about x have an increasing root?

2) When the value of m is taken, the solution of the equation x/(x+3)-(x-1)/(x-3) = m/(x 2-9) about x is negative?

Solution:

When the equation is deformed, it may sometimes produce roots that are not suitable for the original equation, which is called increasing roots of the original equation. Because increasing roots may occur when solving the fractional equation, it is necessary to test the solution of the fractional equation. For the sake of simplicity, when the equation is deformed, the obtained root is usually substituted into the algebraic expression (the simplest common denominator) to see whether its value is 0, so that the root with the algebraic expression of 0 is the increased root of the original equation and must be discarded.

( 1)

5/(x-2)=m/(x^2-4)+3/(x+2)，

It's deformed,

(5x+ 10)/(x^2-4)=(m+3x-6)/(x^2-4)，

So when x 2-4 is not equal to 0, the equation is deformed.

5x+ 10=m+3x-6，

x=m/2 -8，

When m= 12 or 20, x 2-4 is equal to 0, so it is root growth.

(2)x/(x+3)-(x- 1)/(x-3)=m/(x^2-9)

It's deformed,

(-5x+3)/(x^2-9)=m/(x^2-9)

When x 2-9 is not equal to 0, it is deformed.