Question

Упростите выражение.................

Answer 1

$frac{c-1}{c+sqrt{c}+1}:frac{c^{0,5}+1}{c^{1,5}-1}+2c^{frac{1}{2}}=frac{(c^{0,5}-1)(c^{0,5}+1)}{c+c^{0,5}+1}cdot frac{(c^{0,5}-1)(c+c^{0,5}+1)}{c^{0,5}+1}+2c^{0,5}=\\=(c^{0,5}-1)^2+2c^{0,5}=c-2c^{0,5}+1-2c^{0,5}=c+1$


$frac{2(x^{0,25}-y^{0,25})}{x^{-frac{1}{2}}y^{-frac{1}{4}}-x^{-frac{1}{4}}y^{-frac{1}{2}}}-x-y=frac{2(x^{frac{1}{4}}-y^{frac{1}{4}})}{x^{-frac{1}{4}}y^{-frac{1}{4}}(x^{-frac{1}{4}}-y^{-frac{1}{4}})}-x-y=\\=frac{2x^{frac{1}{4}}y^{frac{1}{4}}(x^{frac{1}{4}}-y^{frac{1}{4}})}{frac{y^{frac{1}{4}}-x^{frac{1}{4}}}{x^{frac{1}{4}}y^{frac{1}{4}}}}-x-y=$

$=-2x^{frac{1}{2}}y^{frac{1}{2}}-x-y=$

$=-(x^{frac{1}{2}}+y^{frac{1}{2}}})^2$