Function Expression :
\[f(x)=\frac{2x-3}{x^2-3x} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, 3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \overset{<}{\rightarrow3} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(3 - 2 x\right) \left(2 x - 3\right)}{\left(x^{2} - 3 x\right)^{2}} + \frac{2}{x^{2} - 3 x} \]\[f^{\,\prime}(x)=\frac{- 2 x^{2} + 6 x - 9}{x^{2} \left(x^{2} - 6 x + 9\right)} \]
\[ \]
Integral
\[F(x) = \log{\left(x^{2} - 3 x \right)} \]Sign Table
Variation Table
Plot
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