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Exercises: Rational functions

Bestimme den maximal möglichen Definitionsbereich folgender gebrochenrationaler Funktionen:

$f (x) = \frac{7 x - 3}{8 x - 5}$

For this task you need the following basic knowledge: Definitionsmenge bestimmen
$f (x)$ $=$ $\frac{7 x - 3}{8 x - 5}$
↓
Nenner gleich 0 setzten.
$8 x - 5$ $=$ $0$ $+ 5$
$8 x$ $=$ $5$ $: 8$
$x$ $=$ $\frac{5}{8}$
$D_{f}$ $=$ $ℝ \ {\frac{5}{8}}$
$f (x) = \frac{x^{3}}{{(x - 1)}^{2}} + 7 x$

For this task you need the following basic knowledge: Definitionsmenge bestimmen
$f (x)$ $=$ $\frac{x^{3}}{{(x - 1)}^{2}} + 7 x$
↓
Nenner gleich 0 setzen.
${(x - 1)}^{2}$ $=$ $0$
↓
Definitionslücke ablesen.
$x$ $=$ $1$
$D_{f}$ $=$ $ℝ \ {1}$
$f (x) = \frac{1}{x (x - 5)}$

For this task you need the following basic knowledge: Definitionsmenge bestimmen
$f (x)$ $=$ $\frac{1}{x (x - 5)}$
↓
Nenner gleich 0 setzten.
$x (x - 5)$ $=$ $0$
↓
Lese die Nullstellen ab.
$x_{1}$ $=$ $0$
$x_{2}$ $=$ $5$
$D_{f}$ $=$ $ℝ \ {0; 5}$

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