Multiply $\frac{1}{x+y}$ times $\frac{1}{x-y}$ by multiplying numerator times numerator and denominator times denominator.
$$\frac{1}{\left(x+y\right)\left(x-y\right)}$$
Consider $\left(x+y\right)\left(x-y\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
