Function Expression :
\[f(x)=\frac{x-3}{x^2-2x} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \overset{<}{\rightarrow2} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(2 - 2 x\right) \left(x - 3\right)}{\left(x^{2} - 2 x\right)^{2}} + \frac{1}{x^{2} - 2 x} \]\[f^{\,\prime}(x)=\frac{- x^{2} + 6 x - 6}{x^{2} \left(x^{2} - 4 x + 4\right)} \]
\[ \]
Integral
\[F(x) = \frac{3 \log{\left(x \right)}}{2} - \frac{\log{\left(x - 2 \right)}}{2} \]Sign Table
Variation Table
Plot
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