# How do you simplify (-5+5root4(5))/(3root4(6))?

Aug 8, 2017

$\frac{5 \left(\sqrt[4]{5} - 1\right)}{3 \sqrt[4]{6}} = \frac{5}{18} \left(\sqrt[4]{5} - 1\right) {6}^{\frac{3}{4}}$

#### Explanation:

Given: $\frac{- 5 + 5 \sqrt[4]{5}}{3 \sqrt[4]{6}}$

To simplify factor a $5$ in the numerator: $\frac{5 \left(\sqrt[4]{5} - 1\right)}{3 \sqrt[4]{6}}$

This could be considered a simplified solution, although it is possible to eliminate the denominator knowing that $\sqrt[4]{6} = {6}^{\frac{1}{4}}$. Multiply both numerator and denominator by ${6}^{\frac{3}{4}}$:

$\frac{5 \left(\sqrt[4]{5} - 1\right)}{3 \cdot {6}^{\frac{1}{4}}} \cdot \frac{{6}^{\frac{3}{4}}}{{6}^{\frac{3}{4}}} = \frac{5 \left(\sqrt[4]{5} - 1\right) {6}^{\frac{3}{4}}}{3 \cdot {6}^{\frac{1}{4}} \cdot {6}^{\frac{3}{4}}} = \frac{5 \left(\sqrt[4]{5} - 1\right) {6}^{\frac{3}{4}}}{3 \cdot 6}$

$= \frac{5}{18} \left(\sqrt[4]{5} - 1\right) {6}^{\frac{3}{4}}$