Verified answer

[tex]\displaystyle\bf\\\frac{a^{2}-4b^{2} }{9a^{2} -b^{2} } :\frac{a^{2}+4ab+4b^{2} }{9a^{2} -6ab+b^{2}} \cdot\frac{3a+b}{a-2b} =\\\\\\=\frac{(a-2b)(a+2b)}{(3a-b)(3a+b)} :\frac{(a+2b)^{2} }{(3a-b)^{2} } \cdot\frac{3a+b}{a-2b} =\\\\\\=\frac{(a-2b)(a+2b)}{(3a-b)(3a+b)} \cdot\frac{(3a-b)^{2} }{(a+2b)^{2} } \cdot\frac{3a+b}{a-2b} =\frac{3a-b}{a+2b} \\\\\\\frac{3a-b}{a+2b} =\frac{3a-b}{a+2b}[/tex]

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