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Exercises: Rational functions

Gegeben ist der Bruchterm $T (x) = \frac{1}{x} - \frac{1}{x + 2}$ .

Gib die Definitionsmenge des Terms $T (x) = \frac{1}{x} - \frac{1}{x + 2}$ an.

For this task you need the following basic knowledge: Gebrochenrationale Funktionen
Definitionsmenge bestimmen
$T (x) = \frac{1}{x} - \frac{1}{x + 2}$
$\Rightarrow$ $D_{f} = ℝ \ {- 2; 0}$
Fasse die beiden Brüche zusammen und vereinfache.

For this task you need the following basic knowledge: Gebrochenrationale Funktionen
$T (x)$ $=$ $\frac{1}{x} - \frac{1}{x + 2}$
↓
Hauptnenner bilden
$=$ $\frac{x + 2}{x (x + 2)} - \frac{x}{(x + 2) x}$
$=$ $\frac{x + 2 - x}{(x + 2) x}$
$=$ $\frac{2}{x^{2} + 2 x}$
$\Rightarrow$ $T (x) = \frac{2}{x^{2} + 2 x}$
Berechne T(3).

For this task you need the following basic knowledge: Gebrochenrationale Funktionen
$T (x)$ $=$ $\frac{2}{x^{2} + 2 x}$
↓
3 einsetzen.
$T (3)$ $=$ $\frac{2}{9 + 6}$
$=$ $0,13$
$\Rightarrow T (3) = 0,1 3$

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