perform the indicated operation and if possible simplify. (2x+4y)/(2x^2+5xy+2y^2)*(4x^2-y^2)/(8x^2-8)÷(x^2+4xy+4y^2)/(x^2-6xy+9y^2)

Question

i don't understand this the answer is (2x-y)(x-3y)^2/4(x-1)(x+1)(x+2y)^2

Answer 1

It factors to

2(x+2y)/((2x+1)(x+2)) * (2x-y)(2x+y)/((8(x+1)(x-1)) * (x-3y)(x-3y)/((+2y)(x+2y)) , I changed the division at the end to multiplication by "flipping" the fraction

= (2x-y)(x-3y)^2 / [ 4(x+1)(x-1)(x+2y)^2 ]

= their answer