Упростите выражение (6b^3+48b)/(b^3+64)-(3b^2)/(b^2-4b+16).

Ответ:

\[\frac{6b^{3} + 48b}{b^{3} + 64} - \frac{3b^{2}}{b^{2} - 4b + 16} =\]

\[= \frac{6b^{3} + 48b}{(b + 4)\left( b^{2} - 4b + 16 \right)} - \frac{3{b^{2}}^{\backslash b + 4}}{b^{2} - 4b + 16} =\]

\[= \frac{6b^{3} + 48b - 3b^{3} - 12b^{2}}{(b + 4)\left( b^{2} - 4b + 16 \right)} =\]

\[= \frac{3b^{3} - 12b^{2} + 48b}{(b + 4)\left( b^{2} - 4b + 16 \right)} =\]

\[= \frac{3b(b^{2} - 4b + 16)}{(b + 4)\left( b^{2} - 4b + 16 \right)} = \frac{3b}{b + 4}\]