\(y=\frac{x-3}{x-4}\Rightarrow y'=\frac{-1}{\left(x-4\right)^2}\) ; \(y''=\frac{2}{\left(x-4\right)^3}\)
\(2\left(y'\right)^2=\frac{2}{\left(x-4\right)^4}\)
\(\left(y-1\right)y''=\left(\frac{x-3}{x-4}-1\right).\frac{2}{\left(x-4\right)^3}=\frac{1}{\left(x-4\right)}.\frac{2}{\left(x-4\right)^3}=\frac{2}{\left(x-4\right)^4}\)
\(\Rightarrow2\left(y'\right)^2=\left(y-1\right)y''\)
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