Factor (6x^2-11xy+3y^2)/(2x^2-7xy+6y^2)*(3x^2+8xy+4y^2)/(2y^2-3xy-9x^2)

Question

Please show step by step, I've been stuck on this for hours. I know what the answer is but I have no idea how to solve it.

Answer 1

6x² - 11xy +3y²  · 3x² + 8xy + 4y²

2x² - 7xy + 6y²      2y² - 3xy - 9x²

 

=  (3x - y)(2x - 3y) · (3x + 2y)(x + 2y)

    (2x - 3y)(x - 2y)    (2y  + 3x)(y - 3x)

 

= (3x - y)(2x - 3y) · (3x + 2y)(x + 2y)   =  x + 2y     = x + 2y

   (2x - 3y)(x - 2y)    -(2y + 3x)(3x - y)      -(x - 2y)     2y - x