Question

Упростите выражение.................

Answer 1

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


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

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

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