Докажите тождество (4,5a^2+0,5ab)/(40,5a^2-0,5b^2)=a/(9a-b).

\[\frac{4,5a^{2} + 0,5ab}{40,5a^{2} - 0,{5b}^{2}} = \frac{a}{9a - b}\]

\[\frac{4,5a^{2} + 0,5ab}{40,5a^{2} - 0,5b^{2}} = \frac{a}{9a - b}\]

\[\frac{0,5a(9a + b)}{0,5 \cdot \left( 81a^{2} - b^{2} \right)} = \frac{a}{9a - b}\]

\[\frac{a(9a + b)}{(9a - b)(9a + b)} = \frac{a}{9a - b}\]

\[\frac{a}{9a - b} = \frac{a}{9a - b}\]

\[ч.т.д.\]