Elementary Algebra

$\frac{x-y}{x}$
We factor the expression in the numerator of the second fraction by using the rule $a^{2}-b^{2}=(a+b)(a-b)$. Then, we multiply fractions by multiplying the numerators of the fractions by each other and the denominators of the fractions by each other. Then, we cancel out the resultant common factors in the numerator and the denominator of the two fractions to simplify: $\frac{y}{x+y}\times\frac{x^{2}-y^{2}}{xy}$ =$\frac{y}{x+y}\times\frac{(x+y)(x-y)}{xy}$ =$\frac{y}{1}\times\frac{(x-y)}{xy}$ =$\frac{1}{1}\times\frac{(x-y)}{x(1)}$ =$\frac{x-y}{x}$