Ответ:

Тотожність доведено

[tex] \frac{a}{a {}^{2} + 18a + 81 } \div \frac{a}{9a + 81} + \frac{a}{a + 9} = 1 \\ \frac{a}{(a + 9 ){}^{2} } \times \frac{9a + 81}{a} + \frac{a}{a + 9} = 1 \\ \frac{1}{a + 9} \times 9 + \frac{a}{a + 9} = 1 \\ \frac{9}{a + 9} + \frac{a}{a + 9} = 1 \\ \frac{9 + a}{a + 9} = 1 \\ 1 = 1[/tex]