Решение:

a)

$$\frac{x^{\frac{4}{3}}y + xy^{\frac{4}{3}}}{\sqrt[3]{x} + \sqrt[3]{y}} = \frac{x^{\frac{4}{3}}y + xy^{\frac{4}{3}}}{x^{\frac{1}{3}} + y^{\frac{1}{3}}} = \frac{xy(x^{\frac{1}{3}} + y^{\frac{1}{3}})}{x^{\frac{1}{3}} + y^{\frac{1}{3}}} = xy$$

Ответ: $$xy$$

б)

$$\frac{q^{\frac{1}{3}} - q^{\frac{7}{3}}}{q^{\frac{1}{3}} - q^{\frac{4}{3}}} - \frac{q^{\frac{1}{3}} - q^{\frac{5}{3}}}{q^{\frac{2}{3}} + q^{-\frac{1}{3}}} = \frac{q^{\frac{1}{3}}(1 - q^2)}{q^{\frac{1}{3}}(1 - q)} - \frac{q^{\frac{1}{3}}(1 - q^{\frac{4}{3}})}{q^{-\frac{1}{3}}(q + 1)} = \frac{(1-q)(1+q)}{1-q} - \frac{q^{\frac{2}{3}}(1 - q^{\frac{4}{3}})}{q+1} =$$ $$= 1+q - q^{\frac{2}{3}}q^{-\frac{1}{3}}(1-q) = 1 + q - q^{\frac{1}{3}}(1-q) = 1 + q - q^{\frac{1}{3}} + q^{\frac{4}{3}}$$

Ответ: $$1 + q - q^{\frac{1}{3}} + q^{\frac{4}{3}}$$