Answer
$$\frac{x^2-5yx+4y^2}{x^3+3x^2y+3y^2x+y^3}$$
Work Step by Step
Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find:
$$ \frac{\left(x-y\right)}{x^2+2xy+y^2}\times \frac{x^2-5xy+4y^2}{\left(x^2-y^2\right)}\\ \frac{\left(x-y\right)\left(x-4y\right)}{x^3+3x^2y+3y^2x+y^3}\\ \frac{x^2-5yx+4y^2}{x^3+3x^2y+3y^2x+y^3}$$
