Ensino Médio ⇒ Potências de Expoente Racional Tópico resolvido

[Killin]

Simplifique: [tex3]\frac{x^{\frac{1}{2}}+1}{x+x^{\frac{1}{2}}+1}\div \frac{1}{x^{1,5}-1}[/tex3]

Resposta: x-1.

[csmarceloMOD]

[tex3]\frac{x^{\frac{1}{2}}+1}{x+x^{\frac{1}{2}}+1}\div \frac{1}{x^{1,5}-1}[/tex3]

[tex3]=\frac{\sqrt{x}+1}{x+\sqrt{x}+1}\div \frac{1}{\sqrt{x^3}-1}[/tex3]

[tex3]=\frac{(\sqrt{x}+1)(\sqrt{x}^3-1)}{x+\sqrt{x}+1}[/tex3]

[tex3]=\frac{(\sqrt{x}+1)(\sqrt{x}^3-1^3)}{x+\sqrt{x}+1}[/tex3]

[tex3]=\frac{(\sqrt{x}+1)(\sqrt{x}-1)(x+\sqrt{x}+1)}{x+\sqrt{x}+1}[/tex3]

[tex3]=(\sqrt{x}+1)(\sqrt{x}-1)[/tex3]

[tex3]=\sqrt{x}^2-1^2[/tex3]

[tex3]=x-1[/tex3]