I need to simplify this equation and don't know how, please help! ( (y)/(x) - (x)/(y))/( (1)/(y)-(1)/(x))

Question

I need to simplify this equation and don't know how, please help!


`( (y)/(x) - (x)/(y))/( (1)/(y)-(1)/(x))`

Answer 1

`\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\`


`\bf \cfrac{(y)/(x)-(x)/(y)}{(1)/(y)-(1)/(x)}\implies \cfrac{\textit{LCD of \underline{xy}}}{\textit{LCD of \underline{xy} also}}\implies \cfrac{(y^2-x^2)/(xy)}{(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`