Simplify: (x^4n*y^n - x^n*y^4n)/(x^n*y^3n - x^3n*y^n)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll factor the numerator and denominator by x^n*y^n:
x^n*y^n(x^3n - y^3n)/x^n*y^n(y^2n - x^2n)
We'll reduce and we'll get:
(x^3n - y^3n)/(y^2n - x^2n)
We'll write the numerator using the formula of difference of cubes:
x^3n - y^3n = (x^n - y^n)(x^2n + x^n*y^n + y^2n)
We'll write the denominator using the formula of difference of squares:
y^2n - x^2n = (y^n - x^n)(y^n + x^n) = -(x^n - y^n)(y^n + x^n)
the fraction will become:
(x^3n - y^3n)/(y^2n - x^2n) = (x^n - y^n)(x^2n + x^n*y^n + y^2n)/ -(x^n - y^n)(y^n + x^n)
We'll reduce and we'll get:
-(x^2n + x^n*y^n + y^2n)/(y^n + x^n)

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