№3. Найдите значение выражения: \(\dfrac{a^2-b^2}{a^2}-\dfrac{a}{ab+b^2}\) при \(a=\dfrac12\), \(b=\dfrac23\).

Подставим значения:

\[\frac{a^2-b^2}{a^2}-\frac{a}{ab+b^2}=\frac{\frac14-\frac49}{\frac14}-\frac{\frac12}{\frac12\cdot\frac23+\frac49}.\]

\[\frac{\frac14-\frac49}{\frac14}=\frac{-\frac7{36}}{\frac14}=-\frac79,\qquad \frac{\frac12}{\frac13+\frac49}=\frac{\frac12}{\frac79}=\frac9{14}.\]

\[-\frac79-\frac9{14}=-\frac{98}{126}-\frac{81}{126}=-\frac{179}{126}.\]

Ответ: \(-\dfrac{179}{126}\).