tex]...

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[tex]\frac{(5ab+a^{-3}) ^{2} }{5a^{4} b^{-2}+b^{-3} } -5a^{-2} b^{4}[/tex]

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$\frac{(5ab+a^{-3})^{2}}{5a^{4}b^{-2}+b^{-3}}-5a^{-2}b^{4}=\frac{(5ab+\frac{1}{a^{3}})^{2}}{5a^{4}*\frac{1}{b^{2} }+\frac{1}{b^{3}}}-5*\frac{1}{a^{2}}*b^{4}}=\frac{(\frac{5a^{4}b+1 }{a^{3}})^{2}}{\frac{5a^{4} }{b^{2}}+\frac{1}{b^{3}}}-\frac{5b^{4} }{a^{2} }=\frac{\frac{(5a^{4}b+1)^{2}}{a^{6} }}{\frac{5a^{4}b+1 }{b^{3} }}-\frac{5b^{4} }{a^{2} }=\frac{(5a^{4}b+1)^{2}*b^{3}}{(5a^{4}b+1)*a^{6}}-\frac{5b^{4} }{a^{2} }=\frac{(5a^{4}b+1)*b^{3}}{a^{6} }-\frac{5b^{4} }{a^{2} }=$ $=\frac{5a^{4}b^{4}+b^{3}-5a^{4}b^{4}}{a^{6}}=\frac{b^{3} }{a^{6} }$

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