[tex]\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\\\\
-------------------------------\\\\[/tex]
[tex]\bf \cfrac{\frac{y}{x}-\frac{x}{y}}{\frac{1}{y}-\frac{1}{x}}\implies \cfrac{\textit{LCD of \underline{xy}}}{\textit{LCD of \underline{xy} also}}\implies \cfrac{\frac{y^2-x^2}{xy}}{\frac{x-y}{xy}}\implies \cfrac{y^2-x^2}{\stackrel{ }{xy}}\cdot \cfrac{\stackrel{ }{xy}}{x-y}
\\\\\\
\cfrac{y^2-x^2}{x-y}\implies \cfrac{(y-x)(y+x)}{x-y}\implies \cfrac{\stackrel{ }{(y-x)}(y+x)}{-\stackrel{ }{(y-x)}}\implies \cfrac{y+x}{-1}
\\\\\\
-(y+x)\implies -y-x[/tex]
