Найдите значение дроби (2a^3+2b^3)/(a^2-b^2) при a=2; b=3.

\[\frac{2a^{3} + 2b^{3}}{a^{2} - b^{2}} = \frac{2\left( a^{3} + b^{3} \right)}{a^{2} - b^{2}} =\]

\[= \frac{2(a + b)\left( a^{2} - ab + b^{2} \right)}{(a - b)(a + b)} =\]

\[= \frac{2\left( a^{2} - ab + b^{2} \right)}{a - b};\]

\[a = 2;\ \ b = 3:\]

\[\frac{2(4 - 6 + 9)}{2 - 3} = \frac{14}{- 1} = - 14.\]