[tex]\bf xy^2-x^2y-2=0\qquad (1,-1)\\\\
-------------------------------\\\\
\left( y^2+x2y\cfrac{dy}{dx} \right)-\left( 2xy+x^2\cfrac{dy}{dx} \right)-0=0
\\\\\\
2xy\cfrac{dy}{dx}-x^2\cfrac{dy}{dx}=2xy-y^2\impliedby \textit{common factor}
\\\\\\
\cfrac{dy}{dx}(2xy-x^2)=2xy-y^2\implies \boxed{\cfrac{dy}{dx}=\cfrac{2xy-y^2}{2xy-x^2}}
\\\\\\
\left. \cfrac{2xy-y^2}{2xy-x^2} \right|_{1,-1}\implies \cfrac{-2-1}{-2-1}\implies 1\\\\
-------------------------------\\\\[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-1)=1(x-1)
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y+1=x-1\implies \boxed{y=x-2}[/tex]
