Question 173730
{{{(x^(2n) + 2(x^n)(y^n) - 3y^(2n))/( x^(2n) + 5(x^n)(y^n) - 6y^(2n))}}}


This looks like a horror, but it really isn't that bad.


Let {{{t=x^n}}} and {{{u=y^n}}} then substitute:


{{{(t^2 + 2tu - 3u^2)/( t^2 + 5tu - 6u^2)}}}


Now factor both the numerator and the denominator:


{{{((t-u)(t+3u))/((t-u)(t+6u))}}}


Eliminate the common factor of {{{t-u}}}


{{{(cross((t-u))(t+3u))/(cross((t-u))(t+6u))}}}


Then substitute the original expressions for {{{t}}} and {{{u}}} back into the expression:


{{{(x^n+3y^n)/(x^n+6y^n)}}}


Done.