Question 169906
{{{(x^4-2x^2y^2+y^4)/(x^4-x^3y-xy^3+y^4)}}}
Group terms in the denominator:
{{{(x^4-2x^2y^2+y^4)/((x^4-x^3y)-(xy^3-y^4))}}}
{{{(x^4-2x^2y^2+y^4)/(x^3(x-y)-y^3(x-y))}}}
{{{(x^4-2x^2y^2+y^4)/(x-y)(x^3-y^3)}}}
Factoring the numerator:
{{{(x^2-y^2)(x^2-y^2)/(x-y)(x^3-y^3)}}}
{{{(x-y)(x+y)(x^2-y^2)/(x-y)(x^3-y^3)}}}
{{{(x+y)(x^2-y^2)/(x^3-y^3)}}}
Applying factor for "difference of cubes" in the denominator:
{{{(x+y)(x^2-y^2)/(x-y)(x^2-xy+y^2)}}}
{{{(x+y)(x-y)(x+y)/(x-y)(x^2-xy+y^2)}}}
{{{(x+y)(x+y)/(x^2-xy+y^2)}}}
{{{(x+y)^2/(x^2-xy+y^2)}}}