Posted by **Jenna** on Wednesday, April 25, 2012 at 2:31pm.

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

- algebra -
**Steve**, Wednesday, April 25, 2012 at 4:05pm
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)

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