Пожалуйста упростите данный пример подробно

[latex] \frac{(ab^{-5}-a^{-5}b)^{-1}(a^{-3}+b^{-3})}{(a^{-1}b^{-4}-b^{-1}a^{-4})^{-1}} = \frac{ (\frac{a}{b^5}- \frac{b}{a^5})^{-1}( \frac{1}{a^3}+\frac{1}{b^3}) }{\frac{1}{ab^4}- \frac{1}{a^4b}}=\\\\\\ = \frac{ (\frac{a^6-b^6}{a^5b^5})^{-1} ( \frac{a^3+b^3}{a^3b^3}) }{ (\frac{a^3-b^3}{a^4b^4})^{-1}}= \frac{ \frac{a^5b^5}{a^6-b^6}\cdot \frac{a^3+b^3}{a^3b^3}}{ \frac{a^4b^4}{a^3-b^3} } =\\\\\\ = \frac{a^5b^5}{(a^3+b^3)(a^3-b^3)} \cdot \frac{a^3+b^3}{a^3b^3}\cdot \frac{a^3-b^3}{a^4b^4}= \frac{1}{a^2b^2} [/latex]