Function Expression :
\[f(x)=\frac{2x+2}{x^2+2x-3} \]Domain
\[\left]-\infty, -3\right[ \cup \left]-3, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow-3} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow-3} }f(x) = +\infty \]
\[\lim_{x \overset{<}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(- 2 x - 2\right) \left(2 x + 2\right)}{\left(x^{2} + 2 x - 3\right)^{2}} + \frac{2}{x^{2} + 2 x - 3} \]\[f^{\,\prime}(x)=\frac{2 \left(- x^{2} - 2 x - 5\right)}{x^{4} + 4 x^{3} - 2 x^{2} - 12 x + 9} \]
\[ \]
Integral
\[F(x) = \log{\left(x^{2} + 2 x - 3 \right)} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0055 seconds