(6x-2y)/(x^2+xy-2y^2)-(3x+2y)/(x^2+3xy-4y^2)

Answer 1

x^2+xy-2y^2 = (x+2y)(x-y)
x^2+3xy-4y^2 = (x+4y)(x-y)

so, the LCD = (x+2y)(x+4y)(x-y) and putting it all over that LCD, the numerator then becomes

(6x-2y)(x+4y) - (3x+2y)(x+2y)
= 6x^2 +22xy - 8y^2
- 3x^2 +8xy + 4y^2

= 3x^2 + 14xy - 12y^2

so, the final fraction is

3x^2 + 14xy - 12y^2
-------------------------
(x+2y)(x+4y)(x-y)