Wiki-Quellcode von Lösung Bruchgleichungen

Zuletzt geändert von Stephanie Wietzorek am 2025/11/17 14:11

version	line-number	content
1.1	1	Löse unter Angabe der Definitionsmenge folgende Gleichungen:
	2
	3	1. {{formula}}\frac{10}{x}=5 {{/formula}}
	4
	5	{{formula}}D = \mathbb{R} \backslash \{0\}{{/formula}}
	6	{{formula}}L = \{2\}{{/formula}}
	7
	8
	9	2. {{formula}}\frac{10}{x+1}=5 {{/formula}}
	10
	11	{{formula}}D = \mathbb{R} \backslash \{-1\}{{/formula}}
	12	{{formula}}L = \{1\}{{/formula}}
	13
	14
	15	3. {{formula}}\frac{10}{x+1}=\frac{5}{x-1} {{/formula}}
	16
	17	{{formula}}D = \mathbb{R} \backslash \{-1;1\}{{/formula}}
	18	{{formula}}L = \{3\}{{/formula}}
	19
	20
	21	4. {{formula}}\frac{10}{x+1}=\frac{5x}{x-1}-\frac{5x^2}{x^2-1} {{/formula}}
	22
	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}}
	31
	32
	33	5. {{formula}}\frac{10}{2x+2}=\frac{5}{x+1}-1 {{/formula}}
	34
	35	{{formula}}D = \mathbb{R} \backslash \{-1\}; \quad HN = 2(x+1)=2x+2{{/formula}}
2.2	36	{{formula}}10 = 10 - 2x - 2{{/formula}}
	37	{{formula}}x = -1{{/formula}}
	38	{{formula}}L = \{\} \qquad da -1 \notin D {{/formula}}