Question

Сократите дробь:
(2a / 2a+b - 4a2 / 4a2+4ab+b2) : (2a / 4a2-b2 + 1 / b-2a) * b+2a / 2ab-4a2)

Answer 1

1) 2a/2a+b  - 4a²/(2a+b)² = 2a(2a+b)-4a²/(2a+b)² = 4a²+2ab-4a²/(2a+b)²=
=2ab/(2a+b)²

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

3) 2ab/(2a+b)² * (2a-b)(2a+b)/(-b)= -2a(2a-b)/2a+b

4)  -2a(2a-b)/2a+b * b+2a/2a(b-2a)=2a(b-2a)/2a+b  * b+2a/2a(b-2a) = 
=1

Answer 2

2a/(2a+b)-4a²/(2a+b)²=(4a²+2ab-4a²)/(2a+b)²=2ab/(2a+b)²

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

2ab/(2a+b)² : -b/(2a-b)(2a+b)=-2ab/(2a+b)² *(2a-b)(2a+b)/b=(2ab-4a²)/(2a+b)

-2a(2a-b)*[-(2a+b)/2a(2a-b)=1