Упростите выражение (4b^3+8b)/(b^3-8)-2b^2/(b^2+2b+4).

Ответ:

\[\frac{4b^{3} + 8b}{b^{3} - 8} - \frac{2b^{2}}{b^{2} + 2b + 4} =\]

\[= \frac{4b^{3} + 8b}{(b - 2)\left( b^{2} + 2b + 4 \right)} - \frac{2{b^{2}}^{\backslash b - 2}}{b^{2} + 2b + 4} =\]

\[= \frac{4b^{3} + 8b - 2b^{3} + 4b^{2}}{(b - 2)\left( b^{2} + 2b + 4 \right)} =\]

\[= \frac{2b^{3} + 4b^{2} + 8b}{(b - 2)\left( b^{2} + 2b + 4 \right)} =\]

\[= \frac{2b(b^{2} + 2b + 4)}{(b - 2)(b^{2} + 2b + 4)} = \frac{2b}{b - 2}\]