${\displaystyle \frac{\mathrm{x}}{5+\mathrm{x}}}={\displaystyle \frac{4}{\mathrm{x}+1}}-{\displaystyle \frac{4\mathrm{x}}{(5+\mathrm{x})\cdot (\mathrm{x}+1)}}\backslash hspace\{30mm\}\backslash mathrm\{\backslash dfrac\{x\}\{5+x\}=\backslash dfrac\{4\}\{x+1\}-\backslash dfrac\{4x\}\{(5+x)\backslash cdot(x+1)\}\}$

Für $x=-5x=-5$ und $x=-1x=-1$ sind die Brüche nicht definiert, da der Nenner sonst $00$ wäre.

$\Rightarrow \backslash Rightarrow$ D=$\mathbb{R}\backslash mathbb\{R\}$ \ {$-5;-1-5;-1$}

Mitternachtsformel: $x_{1,2}={\displaystyle \frac{-b\pm \sqrt{b^2-4ac}}{2a}}x\_\{1\{,\}2\}=\backslash dfrac\{-b\backslash pm\backslash sqrt\{b^2-4ac\}\}\{2a\}$

$x_{1,2}={\displaystyle \frac{-1\pm \sqrt{(1{)}^2-4\cdot 1\cdot (-20)}}{2\cdot 1}}x\_\{1\{,\}2\}=\backslash dfrac\{-1\backslash pm\backslash sqrt\{(1)^2-4\backslash cdot\; 1\backslash cdot\; (-20)\}\}\{2\backslash cdot\; 1\}$

$x_{1,2}={\displaystyle \frac{-1\pm \sqrt{1+80}}{2}}x\_\{1\{,\}2\}=\backslash dfrac\{-1\backslash pm\backslash sqrt\{1+80\}\}\{2\}$

$x_{1,2}={\displaystyle \frac{-1\pm 9}{2}}x\_\{1\{,\}2\}=\backslash dfrac\{-1\backslash pm9\}\{2\}$

$x_1=4x\_1=4$

$x_2=-5x\_2=-5$

$x_2=-5\mathrm{\notin }Dx\_2=-5\; \backslash notin\; D$

L= { $44$ }