Let m = (x = a + B radical 2, A.B belongs to q), the experiment proves that M is closed for addition, subtraction, multiplication and division

Let m = (x = a + B radical 2, A.B belongs to q), the experiment proves that M is closed for addition, subtraction, multiplication and division

Let x = a + B √ 2, y = C + D √ 2, where a, B, C, D ∈ Q,
Because QM is closed to addition, subtraction, multiplication and division,
So x + y = (a + C) + (B + D) √ 2 ∈ m,
x-y=(a-c)+(b-d)√2∈M,
xy=(ac+2bd)+(ad+bc)√2∈M,
x/y=(a+b√2）（c-d√2）/（c^2-2d^2)=(ac-2bd)/(c^2-2d^2)+[(bc-ad)/(c^2-2d^2)]√2∈M.

Addition and subtraction of fractions: A-A of b-ab a ^ 2 + B ^ 2

Fraction addition and subtraction: A-1 of a + 1 + 1-A of A-2

（a+1）/(a-1)+(a-2)/(1-a)
=（a+1）/(a-1)-(a-2)/(a-1)
=(a+1-a+2)/(a-1)
=3/(a-1)

In A-B, A-B and a + B, any two integers are selected for addition and subtraction, so that the resulting polynomial can be factorized
Speed!

（1）a²-b²-(a-b)=(a-b)(a-b-1)
(2)a²-b²-(a+b)=(a+b)(a-b-1)
(3)a-b-a-b=-2b