Answer and grading standard 1. Answer the question (* * 10) 1. Simplification: (1) (2) (3) (4). Test center: mixed operation of scores; About integral; The total score is average; The simplest score; The simplest common denominator; Multiplication and division of fractions; Addition and subtraction of fractions. Special topic: calculation problems. Analysis: (1) The deformed addition and subtraction rule is based on the fraction with the same denominator, the denominator remains unchanged, and the numerator is added and subtracted, and finally it can be simplified to the simplest fraction; (2) After expansion according to the distribution law of multiplication, the multiplication is calculated first, and then the similar items are merged; (3) Add and subtract the scores of different denominators first, and then calculate what is in brackets. Then, turn division into multiplication and subtract points. (4) First change division into multiplication, subtraction, and then addition. (1) Original formula = = = = =; (2) The original formula = 3 (x+2)? (x+2)=3x+6﹣x=2x+6； (3) The original formula = []? = ? = ; (4) The original formula =? +=+= = = 1. Comments: This topic mainly examines the mixed operation of fractions, divisor, general fractions, simplest denominator, addition, subtraction, multiplication and division of fractions, and Divison's understanding and mastery. The comprehensive use of these properties for calculation is the key to solve this problem. ① ②. Test center: mixed operation of scores. Special topic: calculation problems. Analysis: ① Perform power operation first, then convert division into multiplication, and finally perform multiplication; ② Use the distribution law of multiplication and the complete square formula to remove the brackets first, and then calculate the division. (﹣ )= ? (﹣ )=﹣ ; ②=[(x) 1+ 1(x) 1+x2+2]÷ 1)=(x)。 In the process of calculation, the symbols should be determined first. At the same time, the mixed operation of fractions is studied. Generally speaking, the mixed operation of fractions is carried out according to the normal operation order, but sometimes it is necessary to use the operation law of multiplication to carry out flexible operation according to the characteristics of the topic. If the result is equal to, find the corresponding value of x and solve the fractional equation. Special topic: calculation problems. Analysis: first simplify the given formula, then list the equation about X according to the result of algebraic formula, and find the value of X. The original formula is = =; From =，get: x 2=2，get x = 2。 Comments: This topic examines the operation of real numbers and the simplified calculation of fractions. In the process of simplifying fractions, we must first make clear the operation order, remove the brackets first, and then multiply and divide the fractions. 4. If, try to find the value of k: the mixed operation of scores. Topic: Calculation problem. Analysis: C=(a+b+d)k③，d=(a+b+c)k④。 Add 123④, and discuss it in two cases: a+b+c+d=0 and not equal to 0, so there are two solutions to k. ∫∴ A = (B+C+D) K. When a+b+c+d=0, ∴b+ c+d =∫a =(b+c+d)k, ∴ A = ∴ AK ∴. Xianning) solve the equation. Test center: Solve fractional equation. Special topic: Equation thought. Analysis: The simplest common denominator can be observed as (x+ 1) (x-2), and the fractional equation can be transformed into an integral equation by multiplying both sides of the equation by the simplest common denominator. Both sides can be multiplied by (x+ 1) (. X=﹣ 1.(7 points) test: when x = ﹣1(x+1) (x ﹣ 2) = 0, x = ﹣1is not original. Yueyang) Solve the equation: | =1. Test center: Solve fractional equation. Special topic: calculation problems. Analysis: The simplest common denominator can be observed as (x-2). Multiply both sides of the equation by the simplest common denominator, and then the fractional equation can be transformed into an integral equation to solve. Denominator, get 4﹣x=x﹣2 (4 points) Solution: x=3 (5 points) Test: substitute x=3 into (x ﹣ 2) = 1 ≠ 0. ∴ x = 3 is the solution of the original equation. (6 Suzhou) Solve the equation: Test center: solving fractional equation by substitution method; Solving quadratic equation by unary decomposition method. Special topic: substitution method. Analysis: The two fractions of the equation have a square relationship. If =t, the original equation will be transformed into t 2-t 2 = 0. Method of substitution will be used to transform it into a univariate quadratic equation about t, and the original equation will be transformed into t 2 by finding t first, then finding x, assuming = t. The solution is x 1=﹣ 1. When t=﹣ 1, it is ﹣ 1 and the solution is x 2 =. After testing, x1=-65438+. Suzhou) It is known that | a | a |1|+= 0 |+= 0, and find the solution of square +bx= 1 The nature of non-negative number: absolute value; Properties of non-negative numbers: arithmetic square root. Special topic: comprehensive questions; Equation thought. Analysis: First, according to the non-negative property, find the values of A and B, and then substitute them into the equation to solve. ∵| A ﹣ 1 |+= 0，∴ A ﹣ 1 = 0，a = 1； B+2 = 0，b = ﹣ 2。 -2x =1,get 2x2+x-1= 0, get x1=-1,x. x 2 =. Comments: This question examines the nature of non-negative numbers: when the sum of several non-negative numbers is 0, these non-negative numbers are all 0. At the same time, when solving the fractional equation, it is necessary to find the root. As shown in the figure, point A and point B are on the number axis, and their corresponding numbers are-4, and the distances from point A and point B to the origin are equal. Find the value of X. Test center: Solve the fractional equation; Absolute value. Topic: Chart types. Analysis: The distance from A to the origin is |-4 | = 4, then the distance from B to the origin is 4, which can be transformed into a fractional equation. From the meaning in the question, = |-4 |, the solution is obtained, which proves to be the solution of the original equation, and the value of ∴x is. Comments: (. (2) The basic idea of solving fractional equation is "transformation idea", that is, transforming fractional equation into integral equation to solve 20 10/0. A middle school in Qinzhou actively responded to the call of "Ten-year Plan of Garden Life in Qinzhou" and organized members to plant 300 trees. The actual number of members participating in tree planting is 1.5 times of the original plan, so the actual per capita tree planting is 2 trees less than the original plan. How many members do you plan to take part in planting trees? Test center: the application of fractional equation. Special topic: application problem. Analysis: Assuming that X members originally planned to participate in tree planting, then 1.5x members actually participated in tree planting, with per capita tree planting =, original per capita tree planting-actual per capita tree planting =2, solve the fractional equation, and the results should be tested. Suppose there are x members who originally planned to participate in planting trees. According to the meaning of the question, X=50 is the root of the original equation. Fifty members plan to take part in tree planting activities. Comments: Finding the appropriate equivalence relation is the key to solve the problem. When solving application problems with fractional equations, there will be two equivalent relationships in general problems. At this time, according to the problem to be solved, one of the equivalence relations is selected as the basis of the column equation, and the other is used to set the unknown. 2. Go to Baidu Library, there are many.
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Update 1: First of all, thank you for your support! At the same time, I also thank the two netizens for their careful answers! Be