3 (x + 1) - 1 / 3 (x-1) = 4 (x-1) - 7 / 2 (x + 1), find X

3 (x + 1) - 1 / 3 (x-1) = 4 (x-1) - 7 / 2 (x + 1), find X

x=2/5

1 2/1:0.4=1.35：x

5.45

（x-1）（x-2）（x-3）（x-4）=0

X = 1 or 2 or 34 or

12345 five playing cards, each adjacent two can be exchanged position, how to do in three exchanges into 54321

1 2 3 4 5 -- 1 2 and 3 4 interchange -- 3 4 1 2 5
3 4 1 2 5 -- 4 1 and 2 5 interchange -- 3 2 5 4 1
3 2 5 4 1 -- 3 2 and 5 4 interchange -- 5 4 3 2 1

How to prove the inequality ln (1 + x) > x / (1 + x)? (x > 0)
We should use the concept of derivative. How to prove it?

Let f (x) = ln (1 + x) - X / (1 + x)
f′(x)=1/(1+x)-1/(1+x)²=[1/(1+x)][1-1/(1+x)]＞0
F (x) increases monotonically at [0, + ∞),
So when x > 0,
F (x) > F (0) = 0, that is ln (1 + x) > x / (1 + x)

Help me to work out a math problem
Minus 2 / 3 to the power of - 2 divided by 9 to the power of - 3 multiplied by 1 / 27 to the power of 2
I need the whole process
0

(2/3)^(-2)/9^(-3)*(1/27)^2
=2^(-2)*3^2*3^6*3^(-6)
=9/4.

Help solve a mathematical geometry problem about circle
There is a circular sheet of iron with a diameter of 1m, from which a maximum sector with a circular angle of 90 ° is to be cut
(1) Find the area of the cut part
(2) What is the radius of the circle at the bottom of the cone

1.S=(90/360)π(1/2)²=π/16
2. Bottom circumference = (3 / 4) * 2 π (1 / 2) = 3 π / 4
Let the radius of the bottom circle be r, then 2 π r = 3 π / 4
∴r=3/8

a. B is a positive real number, AB + A + B = 3, find the maximum value of AB and the value range of (a + b)
Please write down the necessary steps

AB + A + B = 3 > = 2 under the radical sign AB + AB, the solution is ab

The relation between "SiNx = 1 / 2" and "cos2x = 1 / 2" in trigonometric function problem
sinx=1/2 cos2x=1/2
It can be obtained from cos 2x = 1 / 2

cos2x=1-2sin²x
So SiNx = 1 / 2, then cos2x = 1 / 2
And cos2x = 1 / 2
Then SiNx = ± 1 / 2

Plane vector
A. P (a-b) = PA Pb (P belongs to R)
B. PM = PN (P belongs to R), so m = n
C. Human a = QA (human, Q belongs to R, a is not equal to 0), so human = Q
D. (person + Q) = person a + person Q

B. PM = PN (P belongs to R), so m = n is wrong
When p = 0, for any plane vector m, n
PM = PN = zero vector
At this time, we can't deduce M = n