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

*print*Print*list*Cite

### 1 Answer

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)