miniaufgabe.js
==== 2. Mai 2022 bis 6. Mai 2022 ====
=== Donnerstag 5. Mai 2022 ===
Faktorisieren Sie:miniAufgabe("#exofaktorisieren4","#solfaktorisieren4",
[["$-2ax^{2}+8ax+192a$", "$-2a\\left(x^{2}-4x-96\\right) = -2a\\left(x+8\\right) \\cdot \\left(x-12\\right)$"], ["$-3n^{3}x^{2}-60n^{3}x-288n^{3}$", "$-3n^{3}\\left(x^{2}+20x+96\\right) = -3n^{3}\\left(x+8\\right) \\cdot \\left(x+12\\right)$"], ["$-5m^{3}x^{2}+10m^{3}x+600m^{3}$", "$-5m^{3}\\left(x^{2}-2x-120\\right) = -5m^{3}\\left(x-12\\right) \\cdot \\left(x+10\\right)$"], ["$-7n^{3}x^{2}+7n^{3}x+630n^{3}$", "$-7n^{3}\\left(x^{2}-x-90\\right) = -7n^{3}\\left(x-10\\right) \\cdot \\left(x+9\\right)$"], ["$-2e^{2}x^{2}+6e^{2}x+216e^{2}$", "$-2e^{2}\\left(x^{2}-3x-108\\right) = -2e^{2}\\left(x+9\\right) \\cdot \\left(x-12\\right)$"], ["$-7x^{3}-168x^{2}-1008x$", "$-7x\\left(x^{2}+24x+144\\right) = -7x\\left(x+12\\right) \\cdot \\left(x+12\\right)$"], ["$-5x^{4}-135x^{3}-900x^{2}$", "$-5x^{2}\\left(x^{2}+27x+180\\right) = -5x^{2}\\left(x+12\\right) \\cdot \\left(x+15\\right)$"], ["$-2wx^{2}-6wx+108w$", "$-2w\\left(x^{2}+3x-54\\right) = -2w\\left(x-6\\right) \\cdot \\left(x+9\\right)$"], ["$-7a^{2}x^{2}-63a^{2}x+630a^{2}$", "$-7a^{2}\\left(x^{2}+9x-90\\right) = -7a^{2}\\left(x-6\\right) \\cdot \\left(x+15\\right)$"]],
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ruby faktorisieren.rb 4
=== Freitag 6. Mai 2022 ===
Bestimmen Sie den Definitionsbereich der GleichungminiAufgabe("#exodefintionsbereich1","#soldefintionsbereich1",
[["$\\frac{8x+5}{x^{2}+3x-28} = \\frac{3x+4}{x^{2}+6x}$", "Nenner faktorisiert: $\\frac{8x+5}{\\left(x-4\\right) \\cdot \\left(x+7\\right)} = \\frac{3x+4}{\\left(x+0\\right) \\cdot \\left(x+6\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-7,-6,0,4\\}$."], ["$\\frac{8x+4}{x^{2}+8x-9} = \\frac{9x+6}{x^{2}-10x+21}$", "Nenner faktorisiert: $\\frac{8x+4}{\\left(x-1\\right) \\cdot \\left(x+9\\right)} = \\frac{9x+6}{\\left(x-7\\right) \\cdot \\left(x-3\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-9,1,3,7\\}$."], ["$\\frac{8x+3}{x^{2}+4x} = \\frac{8x+2}{x^{2}-11x+28}$", "Nenner faktorisiert: $\\frac{8x+3}{\\left(x+0\\right) \\cdot \\left(x+4\\right)} = \\frac{8x+2}{\\left(x-4\\right) \\cdot \\left(x-7\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-4,0,4,7\\}$."], ["$\\frac{7x+6}{x^{2}-7x} = \\frac{7x+6}{x^{2}+4x-5}$", "Nenner faktorisiert: $\\frac{7x+6}{\\left(x-7\\right) \\cdot \\left(x+0\\right)} = \\frac{7x+6}{\\left(x-1\\right) \\cdot \\left(x+5\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-5,0,1,7\\}$."], ["$\\frac{12x+2}{x^{2}+2x-35} = \\frac{5x+4}{x^{2}+x}$", "Nenner faktorisiert: $\\frac{12x+2}{\\left(x+7\\right) \\cdot \\left(x-5\\right)} = \\frac{5x+4}{\\left(x+0\\right) \\cdot \\left(x+1\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-7,-1,0,5\\}$."], ["$\\frac{12x+3}{x^{2}-9x+18} = \\frac{9x+3}{x^{2}+4x+3}$", "Nenner faktorisiert: $\\frac{12x+3}{\\left(x-6\\right) \\cdot \\left(x-3\\right)} = \\frac{9x+3}{\\left(x+1\\right) \\cdot \\left(x+3\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-3,-1,3,6\\}$."], ["$\\frac{4x+3}{x^{2}+13x+42} = \\frac{7x+6}{x^{2}-10x+9}$", "Nenner faktorisiert: $\\frac{4x+3}{\\left(x+6\\right) \\cdot \\left(x+7\\right)} = \\frac{7x+6}{\\left(x-9\\right) \\cdot \\left(x-1\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-7,-6,1,9\\}$."], ["$\\frac{3x+2}{x^{2}-2x-24} = \\frac{12x+3}{x^{2}+12x+27}$", "Nenner faktorisiert: $\\frac{3x+2}{\\left(x+4\\right) \\cdot \\left(x-6\\right)} = \\frac{12x+3}{\\left(x+9\\right) \\cdot \\left(x+3\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-9,-4,-3,6\\}$."], ["$\\frac{7x+2}{x^{2}-25} = \\frac{12x+6}{x^{2}-2x}$", "Nenner faktorisiert: $\\frac{7x+2}{\\left(x-5\\right) \\cdot \\left(x+5\\right)} = \\frac{12x+6}{\\left(x+0\\right) \\cdot \\left(x-2\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-5,0,2,5\\}$."], ["$\\frac{6x+6}{x^{2}-x-12} = \\frac{10x+5}{x^{2}-2x-63}$", "Nenner faktorisiert: $\\frac{6x+6}{\\left(x+3\\right) \\cdot \\left(x-4\\right)} = \\frac{10x+5}{\\left(x+7\\right) \\cdot \\left(x-9\\right)}$. Daraus folgt $\\mathbb{D} = \\mathbb{R} \\setminus \\{-7,-3,4,9\\}$."]],
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ruby definitionsbereiche.rb 1