Question

34 балла! Подробно! Срочно!

Answer 1

$\frac{x-1}{x^{\frac{3}{4}}+x^{\frac{1}{2}}} \cdot \frac{x^{\frac{1}{2}}+x^{\frac{1}{4}}}{x^{\frac{1}{2}}-1} -x^{\frac{1}{4}} =\\\\=\frac{(x^{\frac{1}{4}}-1)(x^{\frac{1}{4}}+1)(x^{\frac{1}{2}}+1)}{x^{\frac{1}{2}}(x^{\frac{1}{4}}+1)} \cdot \frac{x^{\frac{1}{4}}(x^{\frac{1}{4}}+1)}{(x^{\frac{1}{4}}-1)(x^{\frac{1}{4}}+1)} -x^{\frac{1}{4}}=\\\\= \frac{x^{\frac{1}{2}}+1}{x^{\frac{1}{4}}} -x^{\frac{1}{4}}= \frac{x^{\frac{1}{2}}+1-x^{\frac{1}{2}}}{x^{\frac{1}{4}}} =\frac{1}{x^{\frac{1}{4}}}=x^{-\frac{1}{4}}$