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Wiki-Quellcode von Lösung Bruchgleichungen

Version 2.3 von Stephanie Wietzorek am 2025/11/17 14:06
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1 Löse unter Angabe der Definitionsmenge folgende Gleichungen:
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3 1. {{formula}}\frac{10}{x}=5 {{/formula}}
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5 {{formula}}D = \mathbb{R} \backslash \{0\}{{/formula}}
6 {{formula}}L = \{2\}{{/formula}}
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9 2. {{formula}}\frac{10}{x+1}=5 {{/formula}}
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11 {{formula}}D = \mathbb{R} \backslash \{-1\}{{/formula}}
12 {{formula}}L = \{1\}{{/formula}}
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15 3. {{formula}}\frac{10}{x+1}=\frac{5}{x-1} {{/formula}}
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17 {{formula}}D = \mathbb{R} \backslash \{-1;1\}{{/formula}}
18 {{formula}}L = \{3\}{{/formula}}
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21 4. {{formula}}\frac{10}{x+1}=\frac{5x}{x-1}-\frac{5x^2}{x^2-1} {{/formula}}
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23 {{formula}}D = \mathbb{R} \backslash \{-1;1\}{{/formula}}
24 {{formula}}\frac{10}{x+1}=\frac{5x}{x-1}-\frac{5x^2}{x^2-1} {{/formula}} {{formula}}\quad HN =(x-1)(x+1){{/formula}}
25 {{formula}}=\frac{10(x-1)}{(x+1)(x-1)}=\frac{5x(x+1)}{(x-1)(x+1)}-\frac{5x^2}{x^2-1} |\cdot HN {{/formula}}
26 {{formula}}=10(x-1)=5x(x+1)-5x^2 {{/formula}}
27 {{formula}}=10x-10=5x^2+5x-5x^2 {{/formula}}
28 {{formula}}=5x=10 {{/formula}}
29 {{formula}}=x=2 {{/formula}}
30 {{formula}}L = \{2\}{{/formula}}
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33 5. {{formula}}\frac{10}{2x+2}=\frac{5}{x+1}-1 {{/formula}}
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35 {{formula}}D = \mathbb{R} \backslash \{-1\}; \quad HN = 2(x+1)=2x+2{{/formula}}
36 {{formula}}10 = 10 - 2x - 2{{/formula}}
37 {{formula}}x = -1{{/formula}}
38 {{formula}}L = \{\} \qquad da -1 \notin D {{/formula}}