Calculation of fractions in the second grade of junior high school 1.b/(a-b)+a/(a+b)-2ab/(b^2-a^2) 2.(2a+2)/(a+1)-(a^2-1)/(a^2-2a+1) 3.(x^2-2x)/x^2-1/[x-1-(2x-1/x+1)

The operation of elementary dichotomy
First, we simplify, and evaluate 1 + X / x ^ 2 + X-2 / (X-2 + 3 / x + 2), where x = 1 / 2
Online and so on, to simplify the process, thank you
The brackets in the title are X-2 + 3 / x + 2, (X-2 + 3 / x + 2),

The operation of elementary dichotomy
The three sides of triangle are a, B, C respectively, and satisfy (1 / a) + (1 / b) - (1 / C) = (1 / A + B-C). Please judge the shape of triangle and give proof

Isosceles triangle
1\a+1\b = 1\(a+b-c)+1\c
(a+b)\ab=(a+b)\(ac+bc-c^2)
Because a + B = - 0
ab=ac+bc-c^2
(a-c)(b-c)=0
So a = C or B = C
So wait for the waist

1. When x = √ 3, what is the value of the algebraic formula [x / (x-1) - X / (x + 1)] / (2x) / (1-x)? (1 - √ 3) / 2
2. Find the minimum value of fraction (3x & sup2; + 6x + 5) / (& frac12; X & sup2; + X + 1). - 1
3. Given x = 1 / (√ 5 - 2), then the value of X-1 / X is equal to? 4

(1)[x/(x-1)-x/(x+1)]÷(2x)/(1-x)=[x(x+1)-x(x-1)]/[(x+1)(x-1)]*(1-x)/2x=-1/(x+1）
Substituting x = √ 3, the original formula = - 1 / (√ 3 + 1) = (√ 3-1) / 2 is obtained
(2)(3x^2+6x+5)/[(x^2+2x+2)/2]=2*[3(x^2+2x+2)-1]/(x^2+2x+2)
=6-2/（x^2+2x+2)=6-2/[(x+1)^2+1]
So: the minimum value is 6-2 = 4
(3)x=1/(√5 -2)=√5 +2,1/x=√5 -2
So: X-1 / x = √ 5 + 2 - (√ 5 - 2) = 4

Define new operations
For example: 3 ⁃ 2 = 11 2 ⁃ 3 = 3 4 ⁃ 5 = 21, 9 ⁃ 6 =?

I can't do it, but I'll give you some information. I don't know if you can do it
To define a new operation is to express a new operation with a symbol and a known operation expression. For example, let a △ B = a + B + AB 3 △ 2 = 3 + 2 + 6 = 11 5 △ 5 = 5 + 5 + 25 = 35
Example:
The definition of new operation can be regarded as a kind of mathematical problem, such as: X, Y represents two numbers, and the new operation "*" and "△" are specified as follows: X * y = MX + NY, X △ y = kxy, where m, N, K are natural numbers, 1 * 2 = 5, (2 * 3) △ 4 = 64, and the value of (1 △ 2) * 3 is calculated. We use the analytical method to start with the required problem, and the problem requires the value of (1 △ 2) * 3. First, we need to calculate 1 △ 2. According to the definition of "△ 2", 1 △ 2 = k × 1 × 2 = 2K, Since the value of K is unknown, we must first calculate the value of K. after the value of K is calculated, the value of 1 △ 2 is also calculated. Let's assume that 1 △ 2 = A. (1 △ 2) * 3 = a * 3. According to the definition of "*": a * 3 = ma + 3N, we can calculate the value of a * 3 only when we calculate m and N. therefore, to calculate the value of (1 △ 2) * 3, we must first calculate the value of K, m and n. We can calculate the value of M and N by 1 * 2 = 5, The solution is because 1 * 2 = m × 1 + n × 2 = m + 2n, so there are m + 2n = 5. And because m, n are all natural numbers, so the solutions are: ① when m = 1, n = 2: (2 * 3) when m = 1, n = 2: (2 * 3) when m = 1, n = 2: (2 * 3) when n = 2: (2 * 3) when n = 2: (2 * 3) when n = 2, n = 2: (2 * 3) when (2 * 3) when (2 * 3) when m = 3, n = 1, when n = 1: (2 * 3) when m = 3, when n = 1: (2 * 3) when m = 3, when the n = 3, when n = 1: (2 = 3 = 3 = 3, when (2 * 3) (2 * 3) (2 * 3) (2 * 3) (2 * 3) (2 * 3) (2 * 3) (2 * 3) (2 + 2 + 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2) * 3 = 4 * 3 = 1 × 4 + 2 × 3 = 10

New definition operation
It is stipulated that P △ q = PXP + (P-Q) x2
Find 30 △ (5 △ 3)
The answer is 902

30△（5△3）=30△（25+2×2）=30△29=900+1×2=902

New definition of operation
For any natural number, define n! = 1! × 2! × 3! × N, then 1! × 2! × 3 What is the one digit number of x 100?

For any natural number, define n! = 1! × 2! × 3! × n!,
So 1! × 2! × 3 The one digit number of x 100! Is 0

Who defines new operations

The definition of new operations are compiled by the author, and there is no fixed answer mode. Basically, they are filled in the blanks and so on, which are inclined to incomplete induction. Each symbol can not have a specific meaning at all, and the specific analysis of specific questions

It is stipulated that an operation a ⁃ B = AB + A-B, where a and B are real numbers, then a ⁃ B + (B-A) ⁃ B equals ()
A. a2-bB. b2-bC. b2D. b2-a

A ∧ B + (B-A) ∧ B, = AB + A-B + (B-A) × B + (B-A) - B, = AB + A-B + b2-ab + b-a-b, = b2-b

What does the law of operations mean

It's just some basic formulas
such as
A + B = B + A is called the commutative law of addition
A * BB * a is the commutative law of multiplication
There are many such laws, including vector operation law, matrix operation law and so on

Calculation of fractions in the second grade of junior high school 1.b/(a-b)+a/(a+b)-2ab/(b^2-a^2) 2.(2a+2)/(a+1)-(a^2-1)/(a^2-2a+1) 3.(x^2-2x)/x^2-1/[x-1-(2x-1/x+1)