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
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7x^2+xy-6y^2 -4x^2+3xy-y^2
- (-4x^2-4xy/7-24y^2/7)
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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.