Ejercicios Resueltos de Racionalización

a)  $\displaystyle\frac{\sqrt[3]{x+y}}{\sqrt[5]{x^2y^{13}}}$→$\displaystyle\frac{\sqrt[3]{x+y}}{\sqrt[5]{x^2y^{13}}}\frac{\sqrt[5]{x^3y^{2}}}{\sqrt[5]{x^3y^{2}}}$→$\displaystyle\frac{\sqrt[3]{x+y}\sqrt[5]{x^3y^{2}}}{\sqrt[5]{x^2x^3y^{13}y^2}}$
→$\displaystyle\frac{\sqrt[15]{(x+y)^5(x^3y^{2})^3}}{\sqrt[5]{x^5y^{15}}}$→$\displaystyle\frac{\sqrt[15]{(x+y)^5x^9y^6}}{xy^3}\bullet$

b)  $\displaystyle\frac{a+1}{\sqrt[4]{3(a+1)^3}}$→$\displaystyle\frac{a+1}{\sqrt[4]{3(a+1)^3}}\frac{\sqrt[4]{3^3(a+1)}}{\sqrt[4]{3^3(a+1)}}$
→$\displaystyle\frac{\color{red}{(a+1)}\sqrt[4]{3^3(a+1)}}{{3\color{red}{(a+1)}}}$→$\displaystyle\frac{\sqrt[4]{3^3(a+1)}}{{3}}\bullet$

c)  $\displaystyle\frac{a+1}{a+\sqrt{a+1}}$→$\displaystyle\frac{a+1}{a+\sqrt{a+1}}\frac{a-\sqrt{a+1}}{a-\sqrt{a+1}}$
→$\displaystyle\frac{(a+1)(a-\sqrt{a+1})}{a^2-(\sqrt{a+1})^2}$→$\displaystyle\frac{(a+1)(a-\sqrt{a+1})}{a^2-(a+1)}$
→$\displaystyle\frac{(a+1)(a-\sqrt{a+1})}{a^2-a-1}\bullet$