Racionalização de numerador
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Racionalização de numerador
Pessoal, estou resolvendo uma questão que precisa racionalizar o seguinte:
[latex]\frac{2^{2/3}-\sqrt[3]{x+3}}{x^{2}-1}[/latex]
Até onde sei, precisamos multiplicar o numerador e o denominador por uma versão combinada do numerador. Assim:
[latex]\frac{2^{2/3}-\sqrt[3]{x+3}}{x^{2}-1}*\frac{2^{2/3}+\sqrt[3]{x+3}}{2^{2/3}+\sqrt[3]{x+3}}[/latex]
No entanto, fazendo dessa forma, não consigo chegar a resolução de forma prática. Poderiam me ajudar com os próximos passos? Se possível, de forma didática.
A resposta dessa racionalização é:
![Racionalização de numerador 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)
Agradeço desde já a colaboração.
[latex]\frac{2^{2/3}-\sqrt[3]{x+3}}{x^{2}-1}[/latex]
Até onde sei, precisamos multiplicar o numerador e o denominador por uma versão combinada do numerador. Assim:
[latex]\frac{2^{2/3}-\sqrt[3]{x+3}}{x^{2}-1}*\frac{2^{2/3}+\sqrt[3]{x+3}}{2^{2/3}+\sqrt[3]{x+3}}[/latex]
No entanto, fazendo dessa forma, não consigo chegar a resolução de forma prática. Poderiam me ajudar com os próximos passos? Se possível, de forma didática.
A resposta dessa racionalização é:
Agradeço desde já a colaboração.
Chayenne Tenório- Iniciante
- Mensagens : 34
Data de inscrição : 11/02/2017
Idade : 24
Localização : Rio de Janeiro,Brasil
Re: Racionalização de numerador
A sua técnica funciona para raiz quadrada. Para raiz cúbica tem que usar a propriedade [latex] a^3-b^3 = (a-b)(a^2 +ab+b^2)[/latex] ou [latex] a^3+b^3 = (a+b)(a^2 -ab+b^2)[/latex].
No nosso caso [latex] a = 2^\frac{2}{3}[/latex] e [latex] b = \sqrt[3]{x+3}[/latex] .
No nosso caso [latex] a = 2^\frac{2}{3}[/latex] e [latex] b = \sqrt[3]{x+3}[/latex] .
____________________________________________
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