1、(x^2-4y^2)/(x^2+2xy+y^2)÷(x+2y)/(2x^2+2xy)2、(2x)/(5x-3)÷3/(25x^2-9)×x/(5x+3)

1、(x^2-4y^2)/(x^2+2xy+y^2)÷(x+2y)/(2x^2+2xy)2、(2x)/(5x-3)÷3/(25x^2-9)×x/(5x+3)
1、(x^2-4y^2)/(x^2+2xy+y^2)÷(x+2y)/(2x^2+2xy)
2、(2x)/(5x-3)÷3/(25x^2-9)×x/(5x+3)

1、(x^2-4y^2)/(x^2+2xy+y^2)÷(x+2y)/(2x^2+2xy)2、(2x)/(5x-3)÷3/(25x^2-9)×x/(5x+3)
1、(x^2-4y^2)/(x^2+2xy+y^2)÷(x+2y)/(2x^2+2xy)
=(x+2y）（x-2y）/[(x+y)^2]÷(x+2y)/[2x(x+y)]
=(x+2y）（x-2y）/[(x+y)^2]×[2x(x+y)]/(x+2y)
=[2x(x-2y)]/(x+y)
2、(2x)/(5x-3)÷3/(25x^2-9)×x/(5x+3)
=(2x)/(5x-3)×[（5x-3）(5x+3)]/3×x/(5x+3)
=(2x^2)/3

x^2-4y^2/x^2+2xy+y^2除以x+2y/x^2+xy
=(x-2y)(x+2y)/(x+y)^2除以x+2y/x(x+y)
=x(x-2y)/(x+y)

(x^2-4y^2)/(x^2+2xy+y^2)÷(x+2y)/(2x^2+2xy)

=(x+2y)(x-2y)×2(x+y)
(x+y)^2×(x+2y)

=2(x-2y)
x+y

(2x)/(5x-3)÷3/(25x^2-9)×x/(5x+3)

= 2x ×(5x+3)(5x-3）× x
(5x-3) × 3 ×5x+3
= 2x^2
3