Question

упростите

 

$frac{x^{0.6}-x^{-0.6}}{x^{0.4}+x^{-0.4}+1}+x^{-0.2}$

Answer 1

$frac{x^{0.6}-x^{-0.6}}{x^{0.4}+x^{-0.4}+1}+x^{-0.2} =\\ frac{x^{1.2}-1}{x+x^{0.2}+x^{0.6}}+x^{-0.2} =\\ frac{(x^{0.4}-1)(x^{0.8}+x^{0.4}+1)}{x^{0.2}(1+x^{0.4}+x^{0.8})}+x^{-0.2} =\\ frac{x^{0.4}-1}{x^{0.2}}+frac{1}{x^{0.2}} =\\ frac{x^{0.4}-1+1}{x^{0.2}} =\\ frac{x^{0.4}}{x^{0.2}} =\\ x^{0.4-0.2}=x^{0.2}=x^{frac{1}{5}}=sqrt[5] {x}$