Question

(-4x^2+3xy-y^2)/-(-7x^2-xy+6y^2)/(x^2+4xy-2y^2)

Answer 1

Alright, so we can start off by dividing 
-4x^2+3xy-y^2 by -(-7x^2-xy+6y^2)=7x^2+xy-6y^2 using long division, getting 
     
                                   -4/7
                                    _____________________
7x^2+xy-6y^2              -4x^2+3xy-y^2
                                  - (-4x^2-4xy/7-24y^2/7)
                                    __________________
                                              25xy/7+31y^2/7

Since we can't do anything at this point, we do 
-4/7+(25xy/7+31y^2/7)/(7x^2+xy-6y^2)

At this point, we can divide this by 
(x^2+4xy-2y^2), resulting in
 (-4/7+((25xy/7+31y^2/7)/(7x^2+xy-6y^2)))/((x^2+4xy-2y^2)). After that, we can't use long division since the numerator's top x exponent is 1.