4) Racionaliza los denominadores \( \frac{x}{\sqrt[3]{x^{7}}}= \) \( \frac{9}{\sqrt{15+\sqrt{6}}}= \) \( \frac{\sqrt{a b}}{\sqrt{a b}-\sqrt{a}}= \) Funcion Lineal

Simplify the expression by following steps: - step0: Solution: \(\frac{x}{\left(x^{\frac{7}{3}}\right)}\) - step1: Rewrite the expression: \(\frac{x}{x^{\frac{7}{3}}}\) - step2: Reduce the fraction: \(\frac{1}{x^{\frac{7}{3}-1}}\) - step3: Reduce the fraction: \(\frac{1}{x^{\frac{4}{3}}}\) - step4: Simplify: \(\frac{1}{x\sqrt[3]{x}}\) - step5: Calculate: \(\frac{\sqrt[3]{x^{2}}}{x^{2}}\) Calculate or simplify the expression \( 9/(15+\sqrt(6)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{9}{\left(15+\sqrt{6}\right)}\) - step1: Remove the parentheses: \(\frac{9}{15+\sqrt{6}}\) - step2: Multiply by the Conjugate: \(\frac{9\left(15-\sqrt{6}\right)}{\left(15+\sqrt{6}\right)\left(15-\sqrt{6}\right)}\) - step3: Multiply the numbers: \(\frac{9\left(15-\sqrt{6}\right)}{219}\) - step4: Factor the expression: \(\frac{3\left(15-\sqrt{6}\right)\times 3}{73\times 3}\) - step5: Reduce the fraction: \(\frac{3\left(15-\sqrt{6}\right)}{73}\) - step6: Multiply the numbers: \(\frac{45-3\sqrt{6}}{73}\) Calculate or simplify the expression \( \sqrt(a*b)/(\sqrt(a*b)-\sqrt(a)) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\sqrt{ab}}{\left(\sqrt{ab}-\sqrt{a}\right)}\) - step1: Remove the parentheses: \(\frac{\sqrt{ab}}{\sqrt{ab}-\sqrt{a}}\) - step2: Factor the expression: \(\frac{\sqrt{a}\times \sqrt{b}}{\sqrt{a}\times \left(\sqrt{b}-1\right)}\) - step3: Reduce the fraction: \(\frac{\sqrt{b}}{\sqrt{b}-1}\) - step4: Simplify: \(\frac{b+\sqrt{b}}{b-1}\) Aquí están las soluciones para cada una de las expresiones al racionalizar los denominadores: 1. Para la expresión \( \frac{x}{\sqrt[3]{x^{7}}} \): \[ \frac{x}{\sqrt[3]{x^{7}}} = \frac{\sqrt[3]{x^{2}}}{x^{2}} \] 2. Para la expresión \( \frac{9}{\sqrt{15+\sqrt{6}}} \): \[ \frac{9}{\sqrt{15+\sqrt{6}}} = \frac{45-3\sqrt{6}}{73} \] 3. Para la expresión \( \frac{\sqrt{a b}}{\sqrt{a b}-\sqrt{a}} \): \[ \frac{\sqrt{a b}}{\sqrt{a b}-\sqrt{a}} = \frac{b+\sqrt{b}}{b-1} \] Si necesitas más ayuda o aclaraciones, no dudes en preguntar.