1.c/2ab+b/3a^2c-a/5c^2 2.2x+2+(5/x-1) 3.(a+1/a^2+3a+2)+(a+3/a^2+7a+12) 4.(x/a-y+y/y-x)/(xy/x-y) 5.(3-m/2m-4)/(m+2-5/m-2) 6.(a+1/2a-2 -3/2a^2-2 -a+3/2a+2)* 4a^-4/3 7.(a-b/a+b-a+b/a-b)/(1- a^2+b^2/a^2-2ab+b^2) 8.[(1+ 4/x-2)(x-4+ 4/x)-3]/(4/x -1) 9.[1/a^2 + 1/b^2 + (2/a+b)(1/a+1/b]/[(a+b)^2/ab] 10. Given x ^ 2-3x + 1 = 0, find the value of 1. X + 1 / x 2. X ^ 2 + 1 / x ^ 2 3. X ^ 4 + 1 / x ^ 4 11. Simplify X-2 / x ^ 9-9 (1 + 2x-7 / x ^ 2-4x + 4) / 1 / x + 3 and find the value when x = 2006 12. Simplification (x ^ 2 + 4x + 4 / x ^ 2-6x + 9 - 2 + 9-6x + x ^ 2 / 4 + 4x + x ^ 2) * x ^ 2-x-6 / 4x ^ 2-4x-1 The trouble is to write out the process

1.c/2ab+b/3a^2c-a/5c^2 2.2x+2+(5/x-1) 3.(a+1/a^2+3a+2)+(a+3/a^2+7a+12) 4.(x/a-y+y/y-x)/(xy/x-y) 5.(3-m/2m-4)/(m+2-5/m-2) 6.(a+1/2a-2 -3/2a^2-2 -a+3/2a+2)* 4a^-4/3 7.(a-b/a+b-a+b/a-b)/(1- a^2+b^2/a^2-2ab+b^2) 8.[(1+ 4/x-2)(x-4+ 4/x)-3]/(4/x -1) 9.[1/a^2 + 1/b^2 + (2/a+b)(1/a+1/b]/[(a+b)^2/ab] 10. Given x ^ 2-3x + 1 = 0, find the value of 1. X + 1 / x 2. X ^ 2 + 1 / x ^ 2 3. X ^ 4 + 1 / x ^ 4 11. Simplify X-2 / x ^ 9-9 (1 + 2x-7 / x ^ 2-4x + 4) / 1 / x + 3 and find the value when x = 2006 12. Simplification (x ^ 2 + 4x + 4 / x ^ 2-6x + 9 - 2 + 9-6x + x ^ 2 / 4 + 4x + x ^ 2) * x ^ 2-x-6 / 4x ^ 2-4x-1 The trouble is to write out the process

1.c/2ab+b/3a^2c-a/5c^2=(15a*c^2+10b^2-6a^3*b)/30a^2*b*c^22.2x+2+(5/x-1)=2x+5/x+13.(a+1/a^2+3a+2)+(a+3/a^2+7a+12)=(a+2)+(a+4)=2a+64.[x/(x-y)+y/(y-x)]/(xy/x-y)=1/y+1/x5.[(3-m)/(2m-4)]/[m+2-5/(m-2)]=-1/2...

Solving a problem of adding and subtracting fractions in the first grade of junior high school
If a / x + 1 + B / X-1 = 2x + 3 / (x + 1) (x-1) (where a and B are constants), then a = b =?

On the left side, a (x-1) + B (x + 1) = (a + b) x - (B-A)
Compared with the right side of the molecule
A+B=2
B-A=3
A=-0.5
B=2.5

The addition and subtraction of the first fraction of junior high school
1.2/(x-1)-(x+1)/(x-1)
2.2a/(a^-4）-1/（a-2）
3.3x/(x-3)^2+x/(x-3)
4.【2a/(x-2)-x(x+2)】*(x^2-4)/x

1.2/(x-1)-(x+1)/(x-1)=[2-(x+1)]/(x-1)=(-x+1)/(x-1)=-(x-1)/(x-1)=-12.2a/(a^2-4）-1/（a-2）=2a/(a+2)(a-2)-(a+2)/(a+2)(a-2)=(2a-a-2)/(a+2)(a-2)=(a-2)/(a+2)(a-2)=1/(a+2)3.3x/(x-3)^2+x/(x-3)=3x/(x-3)^2+x(x...

On the addition and subtraction of 10.4 fractions in classroom exercise paper (3)
If A2B = 3, then (A3 / B2) 2 / (A / B3) 3 is equal to =?

So a = 3, B = 3, B = 3, B = 3, B = 3, B = 3, B = 3, B = 3, B = 3, B = 3, B and B will bring a and B into 3, and then, a and B will bring a and B into 3 ▔▔▔▔▔ ▔▔ 2B × 3, and bring a and B and B and B into 3 ᥸ 3, 3 ▔▔▔▔▔▔▔▔▔▔▔so (A3 / B2) 2 / (A / B3) 3 = 3

Addition and subtraction of mathematical fraction 2
[3 / (X -- 2) (x + 1)] - (1 / X -- 2) pay attention to the minus sign in the middle, not the title. I only know that the answer is - 1 / x + 1. Ask the great God to answer

Original formula = 3 / (X-2) (x + 1) - (x + 1) / (X-2) (x + 1)
=(3-x-1)/(x-2)(x+1)
=-(x-2)/(x-2)(x+1)
=-1/(x+1)

Mathematics; addition and subtraction of fractions
If B + 1 / C = 1, C + 1 / a = 1, ask the value of AB + 1 / b
Given y = x2 + 2x + 1 / x2-1 divided by X + 1 / x2-x - x + 1, try to explain that no matter what the value of X is, the value of Y remains unchanged
The first question is: B + (1 / C) = 1, C + (1 / a), ask the value of AB + 1 / b.

B + 1 / C = 1, B = 1-1 / C, C + 1 / a = 1, C = 1-1 / a (AB + 1) / b = a + 1 / b = a + 1 / (1-1 / C) = a + C / (C-1) = a + (1-1 / a) / [(1-1 / a) - 1] = a + [(A-1) / a] / (- 1 / a) = a + [- (A-1)] = 1y = x2 + 2x + 1 / x2-1 divide x + 1 / x2-x - x + 1 = (x + 1) ^ 2 / [(x + 1) (x-1)] * x (x-1) / (x + 1) - X

Mathematical problems (addition and subtraction of fractions)
A purchaser went to a feed company twice to buy feed, and spent 800 yuan each time. It is known that the price of feed purchased by the purchaser twice is different, which is m yuan / kg and N yuan / kg respectively. The average price of feed purchased by the purchaser twice is calculated
Write down the specific process

I bought 800 / M and 800 / N kg twice, and spent 800 * 2 yuan
Average price = 2 * 800 / (800 / M + 800 / N) = 2Mn (M + n)

The seventh grade mathematics fraction addition and subtraction exercise 9.2, seeks the process the computation question (on 101 pages of the book 6.7 big questions) century publication
1. A + B + 2B & # 178; divided by (a-b)
6.7 two questions

Is it (a + B + 2B & # 178;) / (a-b)? Or a + B + 2B & # 178; / (a-b)?
If it's the first one, the molecule subtracts B from a and then adds B, and the final result is 1 + 2B (B + 1) / (a-b)
If it is the second result, it should be (A & # 178; - B & # 178; + 2B & # 178;) / (a-b) = (A & # 178; + B & # 178;) / (a-b)

Knowledge structure chart of fraction, decimal and ratio in Grade 6 of primary school

Divide the numerator of a fraction by the denominator to get a decimal. For example, one divided by two is equal to 0.5. Move the decimal point to two places to the right, and then add the percent sign to get the percentage. For example, 0.2 is equal to 20%. Changing the percentage into a decimal is the same as changing the decimal into a percentage, but the two are just the opposite

Primary school score problem, itinerary problem knowledge points

1. The problem of sum and difference is to find the sum and difference of two numbers
(sum + difference) 2 = large number, (sum difference) 2 = decimal number
2. In the sum multiple problem, we know the sum of two numbers and the multiple relation of the two numbers, and then we can find the two numbers
Sum (multiple + 1) = 1 multiple (or decimal), decimal × multiple = large, and - decimal = large
3. In the problem of difference multiple, we know the difference of two numbers and the multiple relation of the two numbers, then we can find the two numbers
Difference (multiple - 1) = decimal, decimal + difference = large
4. Bridge problem, from the front of the bridge, to the rear of the bridge, to find the time
Distance = bridge length + train length
5. The problem of running water is to find out the sailing time of a ship in running water
Ship speed + water speed = downstream speed, ship speed - water speed = upstream speed
9. Age problem, seek the age of two people
Adult age - child age = age difference
11. The clock problem is to find the time when the hour hand and minute hand coincide, form a straight line or right angle
Coincidence time of two needles = number of spaces between two needles △ 11 / 12
The linear time of two needles = (interval number of two needles ± 30) △ 11 / 12
The right angle time of two needles = (the interval between two needles ± 15 or 45) △ 11 / 12
12. The problem of normalization is to find out a single quantity first and then other quantities
13. Sum up the problem, first find the total quantity, and then find other quantities
14. Time difference problem, calculate the time difference from a few days to a few days
First calculate the first and last months, then calculate the middle months
15. Predict the day of the week, known today is the day of the week, how many days after the calculation is the day of the week
Divide the number of days passed by 7 to find the remaining days, and then calculate the day of the week
4. [formula of average problem]
Total quantity △ total copies = average
5. [formula of general travel problem]
Average speed × time = distance;
Distance △ time = average speed;
Distance / average speed = time
6. [formula of reverse travel problem] the reverse travel problem can be divided into two types: "meeting problem" (two people start from two places and walk in opposite directions) and "separation problem" (two people walk in opposite directions). Both of these problems can be solved by the following formula
(speed and) × encounter (departure) time = encounter (departure) distance;
Distance of encounter (departure) / (speed sum) = encounter (departure) time;
Distance of meeting (leaving) and time of meeting (leaving) = speed and distance
　　
7. [formula of travel in the same direction]
Catch up (pull out) distance (speed difference) = catch up (pull out) time;
Catch up (pull away) distance △ catch up (pull away) time = speed difference;
(speed difference) × overtaking time = overtaking distance
8. [formula of train crossing bridge problem]
(bridge leader + train leader) △ speed = bridge crossing time;
(bridge leader + train leader) △ bridge crossing time = speed;
Speed × crossing time = the sum of bridge and vehicle length
9. [formula of sailing problem]
(1) General formula:
Static water speed (ship speed) + current speed (water speed) = downstream speed;
Ship speed water speed = upstream speed;
(downstream speed + upstream speed) △ 2 = ship speed;
(downstream velocity - upstream velocity) 2 = water velocity
(2) The formula of two ships sailing in opposite directions:
Ship a's downstream speed + ship B's upstream speed = ship a's still water speed + ship B's still water speed
(3) The formula of two ships sailing in the same direction:
The static water velocity of fore (AFT) ship - the static water velocity of fore (AFT) ship = the speed of narrowing (widening) the distance between two ships
After calculating the speed of the distance between the two ships, answer the question according to the above formula
10. [engineering problem formula]
(1) General formula:
Work efficiency × working hours = total amount of work;
Total amount of work △ working hours = work efficiency;
Total amount of work △ work efficiency = working hours
(2) The formula for solving engineering problems by assuming that the total amount of work is "1" is as follows
1 △ working time = fraction of the total amount of work completed in unit time;
1 △ what percentage of work can be completed per unit time = working time
(Note: to solve engineering problems with hypothesis method, you can arbitrarily assume that the total amount of work is 2, 3, 4, 5 Especially when the total amount of work is assumed to be the least common multiple of several working hours, the fractional engineering problem can be transformed into a relatively simple integer engineering problem, and the calculation will become relatively simple.)
11. [profit and loss formula]
Profit and loss problem, to find the number of distribution
The difference in the number of surplus goods △ the difference in the number of distribution methods = the number of people allocated
(1) If there is surplus (surplus) at one time and insufficient (deficit) at one time, the following formula can be used:
(profit + loss) / (the difference between the two distributions) = the number of people
For example, "each child has 10 peaches less than 9, and each child has 8 peaches more than 7. Question: how many children and how many peaches are there?"
Solution (7 + 9) △ 10-8) = 16 △ 2 = 8 (pieces) Number of people
10 × 8-9 = 80-9 = 71 Peach
Or 8 × 8 + 7 = 64 + 7 = 71
(2) There is surplus (surplus) in two times
(big profit - small profit) / (the difference between the number of people allocated twice) = the number of people
For example, "when soldiers carry bullets for marching training, each person carries 45 rounds, an additional 680 rounds; if each person carries 50 rounds, an additional 200 rounds will be provided. Question: how many soldiers are there? How many bullets are there?"
Solution (680-200) △ 50-45) = 480 △ 5 = 96 (person)
45 × 96 + 680 = 5000 or 50 × 96 + 200 = 5000
(3) Two times are not enough
(big loss - small loss) / (the difference between the number of people allocated twice) = the number of people
For example, "if you distribute a batch of books to students, each of them will receive 10 copies, with a difference of 90 copies; if each of them receives 8 copies, there will still be a difference of 8 copies. How many students and how many copies are there?"
Solution (90-8) / (10-8) = 82 / 2 = 41 (person)
10 × 41-90 = 320
(4) One time is not enough (loss), and the other time is just finished
Deficit (the difference between the number of people allocated twice) = the number of people
(5) There is surplus (surplus) in one time, and it is just finished in the other time
Surplus (the difference between the two distributions) = number of people
(example omitted)
12. [formula of chicken rabbit problem]
Chicken and rabbit problem, known the total number of chicken and rabbit head and total number of legs, find the number of chickens and rabbits
Number of rabbits = (total number of legs - total number of heads × 2) △ 2,
The number of chickens = (total number of heads × 4-total number of legs) △ 2
(1) Given the total number of heads and feet of chickens and rabbits, find out the number of chickens and rabbits
Number of rabbits = (total feet - feet per chicken × total head) / (feet per rabbit - feet per chicken);
Number of chickens = total number of rabbits
Or is it
Number of chickens = (number of feet per rabbit × number of heads - number of feet) / (number of feet per rabbit - number of feet per chicken)
Number of rabbits = total number of chickens
For example, "there are 36 chickens and rabbits. They have 100 feet. How many chickens and rabbits are there?"
Jieyi
(100-2 × 36) / (4-2) = 14 (pieces) Rabbits;
36-14 = 22 Chicken
Solution 2
(4 × 36-100) / (4-2) = 22 (pieces) Chicken;
36-22 = 14 Rabbit
(2) When the total number of feet of chicken is more than that of rabbit, the formula can be used
(the number of feet per chicken × the difference between the total number of heads and the number of feet) / (the number of feet per chicken + the number of feet per rabbit) = the number of rabbits;
Total head rabbit = chicken
or
(the difference between the number of feet per rabbit × the total number of heads + the number of feet per rabbit) / (the number of feet per chicken + the number of feet per rabbit) = the number of chickens;
Total head number chicken number = rabbit number
(3) Given the difference between the total number and the number of feet of chickens and rabbits, the formula can be used when the total number of feet of rabbits is more than that of chickens
(the number of feet per chicken × the total number of heads + the difference between the number of feet per chicken and rabbit) / (the number of feet per chicken + the number of feet per rabbit) = the number of rabbits;
Total head count - Rabbit count = chicken count
or
(the number of feet of each rabbit × the total number of heads - the difference between the number of feet of chickens and rabbits) / (the number of feet of each chicken + the number of feet of each rabbit) = the number of chickens;
Total head number chicken number = rabbit number
(4) The following formula can be used to solve the problem of gain and loss
(score of 1 qualified product × total number of products - total score of actual products) / (score of each qualified product + deduction score of each unqualified product) = unqualified